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Abstract parabolic evolution equations and Lojasiewicz-Simon inequality . II Applications / / Atsushi Yagi
| Abstract parabolic evolution equations and Lojasiewicz-Simon inequality . II Applications / / Atsushi Yagi |
| Autore | Yagi Atsushi <1951-> |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | ℗♭2021 |
| Descrizione fisica | 1 online resource (IX, 128 p. 607 illus.) |
| Disciplina | 515.353 |
| Collana | SpringerBriefs in mathematics |
| Soggetto topico |
Anàlisi matemàtica
Anàlisi funcional Teoria de la mesura Evolution equations |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-2663-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model. |
| Record Nr. | UNISA-996466413003316 |
Yagi Atsushi <1951->
|
||
| ℗♭2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Abstract parabolic evolution equations and Lojasiewicz-Simon inequality . II Applications / / Atsushi Yagi
| Abstract parabolic evolution equations and Lojasiewicz-Simon inequality . II Applications / / Atsushi Yagi |
| Autore | Yagi Atsushi <1951-> |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | ℗♭2021 |
| Descrizione fisica | 1 online resource (IX, 128 p. 607 illus.) |
| Disciplina | 515.353 |
| Collana | SpringerBriefs in mathematics |
| Soggetto topico |
Anàlisi matemàtica
Anàlisi funcional Teoria de la mesura Evolution equations |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-2663-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model. |
| Record Nr. | UNINA-9910495248303321 |
|
Yagi Atsushi <1951->
|
||
| ℗♭2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combined measure and shift invariance theory of time scales and applications / / Chao Wang, Ravi P. Agarwal
| Combined measure and shift invariance theory of time scales and applications / / Chao Wang, Ravi P. Agarwal |
| Autore | Zhao Bingxuan |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (443 pages) |
| Disciplina | 381 |
| Collana | Developments in Mathematics |
| Soggetto topico |
Differential equations
Equacions diferencials Anàlisi funcional Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-11619-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Riemann Integration, Stochastic Calculus, and Shift Operators on Time Scales -- 1.1 Riemann Integration on Time Scales -- 1.1.1 Riemann Delta and Nabla Integration on Time Scales -- 1.1.2 Some Fundamental Results of the Riemann Integral -- 1.1.3 Fundamental Theorems of Calculus -- 1.2 Stochastic Calculus and Dynamic Equations on Time Scales -- 1.2.1 Relation Between Classical Integrable Functions and Δ-Integrable Functions -- 1.2.2 Stochastic Calculus -- 1.2.3 Stochastic Dynamic Equations on Time Scales -- 1.3 Shift Operators on Time Scales -- 1.3.1 Shift Operators -- 1.3.2 Periodicity of Time Scales -- 1.4 Combined Dynamic Derivatives on Time Scales -- 1.4.1 Delta and Nabla Derivatives -- 1.4.2 Diamond-α Dynamic Derivative -- 1.4.3 Some Basic Properties of Combined Dynamic Derivatives -- 1.4.4 Combined Dynamic Integrations -- 1.5 Combined Liouville Formula and α-Matrix Exponential Solutions -- 1.5.1 Liouville Formula for Δ-Dynamic Equations -- 1.5.2 Liouville Formula for -Dynamic Equations and Some Lemmas -- 1.5.3 Liouville Formula for Diamond-α Dynamic Equations -- 1.6 Quaternion Combined Impulsive Matrix Dynamic Equation on Time Scales -- 1.6.1 Quaternion Delta and Nabla Exponential Function -- 1.6.2 Quaternion Matrix Diamond-Exponential Function and Quaternion Combined Matrix Dynamic Equation -- 1.6.3 Quaternion Impulsive Nonhomogeneous Matrix Combined Dynamic Equation -- 2 α-Measurability and Combined Measure Theory on Time Scales -- 2.1 Lebesgue Measurable and Lebesgue α-Measurable Sets -- 2.1.1 α-Measure -- 2.1.2 Lebesgue Measurable and Lebesgue α-Measurable Sets -- 2.2 α-Measurable Functions and Lebesgue Measurable Functions -- 2.2.1 α-Measurable Functions -- 2.2.2 Lebesgue Measurable and Lebesgue α-Measurable Functions -- 2.3 α-Integral on Time Scales -- 2.3.1 Riemann α-Integral.
2.3.2 Lebesgue α-Integral on Time Scales -- 2.3.3 Relation Between Lebesgue α-Integral and Riemann α-Integral -- 2.4 Lebesgue-Stieltjes Combined α-Measure and Integral on Time Scales -- 2.4.1 Lebesgue-Stieltjes α-Outer Measure and Related Properties -- 2.4.2 Lebesgue-Stieltjes α-Measure and Related Properties -- 2.4.3 Relationships, Extensions, and Composition Theorems for Lebesgue-Stieltjes α-Measure -- 2.5 Lebesgue-Stieltjes α-Measurable Function and α-Integral -- 2.5.1 Lebesgue-Stieltjes α-Measurable Function and Convergence Theorems -- 2.5.2 Lebesgue-Stieltjes α-Integral -- 2.5.3 Relationships, Extensions, and Composition Theorems of Lebesgue-Stieltjes α-Integral -- 3 Shift Invariance and Matched Spaces of Time Scales -- 3.1 Periodic Time Scales with Shift Operators -- 3.2 Singularity of Time Scales Under Action of Shift Operators δ -- 3.3 Complete-Closed Time Scales Under Shifts -- 3.4 The Matched Space of Time Scales and Shift Invariance -- 3.5 Singularity of Time Scales Under Action of Shift Operators δ and δ-1 -- 3.6 Singularity Avoiding: A Shift with Direction -- 4 Almost Periodic Functions Under Matched Spaces of Time Scales -- 4.1 Periodic Functions Under Complete-Closed Time Scales in Shifts -- 4.2 δ-Almost Periodic Functions Under Matched Spaces -- 4.3 Piecewise δ-Almost Periodic Stochastic Process in Shift Operators -- 4.4 n0-Order Δ-Almost Periodic Functions -- 5 Almost Automorphic Functions Under Matched Spaces of Time Scales -- 5.1 Weighted Pseudo δ-Almost Automorphic Functions Under Matched Spaces -- 5.2 n0-Order Weighted Pseudo Δ-Almost Automorphic Functions -- 5.3 Discontinuous Weighted Pseudo S-Almost Automorphic Functions -- 5.3.1 S-Equipotentially Almost Automorphic Sequence Under S-CCTS -- 5.3.2 S-Almost Automorphic Functions and Weighted Pseudo S-Almost Automorphic Functions. 6 C0-Semigroup and Stepanov-Like Almost Automorphic Functions on Hybrid Time Scales -- 6.1 C0-Semigroup on a Quantum Time Scale -- 6.2 Stepanov-Like Almost Automorphic Functions on a Quantum Time Scale -- 6.3 Weak Almost Automorphy on a Quantum Time Scale -- 6.4 Shift-Semigroup Under Matched Spaces of Time Scales -- 6.5 Stepanov-Like Almost Automorphic Functions in Matched Spaces of Time Scales -- 7 Almost Periodic Dynamic Equations Under Matched Spaces -- 7.1 Basic Theory of Nonlinear Almost Periodic Dynamic Equations -- 7.2 Exponential Dichotomy of Inhomogeneous Dynamic Equations -- 7.3 δ-Almost Periodic Solutions of Dynamic Equations -- 7.4 n0-Order Δ-Almost Periodic Solutions for Dynamic Equations -- 8 Almost Automorphic Dynamic Equations Under Matched Spaces -- 8.1 Weighted Pseudo δ-Almost Automorphic Solutions for Dynamic Equations -- 8.2 n0-Order Weighted Pseudo Δ-Almost Automorphic Solutions for Dynamic Equations -- 8.3 Almost Automorphic Impulsive Dynamic Equations Based on Shift Operators -- 9 Applications to Dynamics Models Under Matched Spaces -- 9.1 Almost Periodic Neutral Impulsive Stochastic Lasota-Wazewska Timescale Model -- 9.1.1 Introduction and Model Description -- 9.1.2 Inverse Representation of the Neutral Term with Shift Operator -- 9.1.3 Existence of Mean-Square Almost Periodic Solution -- 9.2 Almost Periodic Impulsive Stochastic Nicholson's Blowflies Timescale Model -- 9.2.1 Model Description -- 9.2.2 Almost Periodic Stochastic Process Under Periodic Time Scales with Shifts δ -- 9.2.3 Mean-Square Positive Almost Periodic Solutions to the Model with Shift Operators -- 9.3 A Numerical Example and the Model on the Quantum Time Scale -- References -- Index. |
| Record Nr. | UNINA-9910595037203321 |
|
Zhao Bingxuan
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combined measure and shift invariance theory of time scales and applications / / Chao Wang, Ravi P. Agarwal
| Combined measure and shift invariance theory of time scales and applications / / Chao Wang, Ravi P. Agarwal |
| Autore | Zhao Bingxuan |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (443 pages) |
| Disciplina | 381 |
| Collana | Developments in Mathematics |
| Soggetto topico |
Differential equations
Equacions diferencials Anàlisi funcional Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-11619-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Riemann Integration, Stochastic Calculus, and Shift Operators on Time Scales -- 1.1 Riemann Integration on Time Scales -- 1.1.1 Riemann Delta and Nabla Integration on Time Scales -- 1.1.2 Some Fundamental Results of the Riemann Integral -- 1.1.3 Fundamental Theorems of Calculus -- 1.2 Stochastic Calculus and Dynamic Equations on Time Scales -- 1.2.1 Relation Between Classical Integrable Functions and Δ-Integrable Functions -- 1.2.2 Stochastic Calculus -- 1.2.3 Stochastic Dynamic Equations on Time Scales -- 1.3 Shift Operators on Time Scales -- 1.3.1 Shift Operators -- 1.3.2 Periodicity of Time Scales -- 1.4 Combined Dynamic Derivatives on Time Scales -- 1.4.1 Delta and Nabla Derivatives -- 1.4.2 Diamond-α Dynamic Derivative -- 1.4.3 Some Basic Properties of Combined Dynamic Derivatives -- 1.4.4 Combined Dynamic Integrations -- 1.5 Combined Liouville Formula and α-Matrix Exponential Solutions -- 1.5.1 Liouville Formula for Δ-Dynamic Equations -- 1.5.2 Liouville Formula for -Dynamic Equations and Some Lemmas -- 1.5.3 Liouville Formula for Diamond-α Dynamic Equations -- 1.6 Quaternion Combined Impulsive Matrix Dynamic Equation on Time Scales -- 1.6.1 Quaternion Delta and Nabla Exponential Function -- 1.6.2 Quaternion Matrix Diamond-Exponential Function and Quaternion Combined Matrix Dynamic Equation -- 1.6.3 Quaternion Impulsive Nonhomogeneous Matrix Combined Dynamic Equation -- 2 α-Measurability and Combined Measure Theory on Time Scales -- 2.1 Lebesgue Measurable and Lebesgue α-Measurable Sets -- 2.1.1 α-Measure -- 2.1.2 Lebesgue Measurable and Lebesgue α-Measurable Sets -- 2.2 α-Measurable Functions and Lebesgue Measurable Functions -- 2.2.1 α-Measurable Functions -- 2.2.2 Lebesgue Measurable and Lebesgue α-Measurable Functions -- 2.3 α-Integral on Time Scales -- 2.3.1 Riemann α-Integral.
2.3.2 Lebesgue α-Integral on Time Scales -- 2.3.3 Relation Between Lebesgue α-Integral and Riemann α-Integral -- 2.4 Lebesgue-Stieltjes Combined α-Measure and Integral on Time Scales -- 2.4.1 Lebesgue-Stieltjes α-Outer Measure and Related Properties -- 2.4.2 Lebesgue-Stieltjes α-Measure and Related Properties -- 2.4.3 Relationships, Extensions, and Composition Theorems for Lebesgue-Stieltjes α-Measure -- 2.5 Lebesgue-Stieltjes α-Measurable Function and α-Integral -- 2.5.1 Lebesgue-Stieltjes α-Measurable Function and Convergence Theorems -- 2.5.2 Lebesgue-Stieltjes α-Integral -- 2.5.3 Relationships, Extensions, and Composition Theorems of Lebesgue-Stieltjes α-Integral -- 3 Shift Invariance and Matched Spaces of Time Scales -- 3.1 Periodic Time Scales with Shift Operators -- 3.2 Singularity of Time Scales Under Action of Shift Operators δ -- 3.3 Complete-Closed Time Scales Under Shifts -- 3.4 The Matched Space of Time Scales and Shift Invariance -- 3.5 Singularity of Time Scales Under Action of Shift Operators δ and δ-1 -- 3.6 Singularity Avoiding: A Shift with Direction -- 4 Almost Periodic Functions Under Matched Spaces of Time Scales -- 4.1 Periodic Functions Under Complete-Closed Time Scales in Shifts -- 4.2 δ-Almost Periodic Functions Under Matched Spaces -- 4.3 Piecewise δ-Almost Periodic Stochastic Process in Shift Operators -- 4.4 n0-Order Δ-Almost Periodic Functions -- 5 Almost Automorphic Functions Under Matched Spaces of Time Scales -- 5.1 Weighted Pseudo δ-Almost Automorphic Functions Under Matched Spaces -- 5.2 n0-Order Weighted Pseudo Δ-Almost Automorphic Functions -- 5.3 Discontinuous Weighted Pseudo S-Almost Automorphic Functions -- 5.3.1 S-Equipotentially Almost Automorphic Sequence Under S-CCTS -- 5.3.2 S-Almost Automorphic Functions and Weighted Pseudo S-Almost Automorphic Functions. 6 C0-Semigroup and Stepanov-Like Almost Automorphic Functions on Hybrid Time Scales -- 6.1 C0-Semigroup on a Quantum Time Scale -- 6.2 Stepanov-Like Almost Automorphic Functions on a Quantum Time Scale -- 6.3 Weak Almost Automorphy on a Quantum Time Scale -- 6.4 Shift-Semigroup Under Matched Spaces of Time Scales -- 6.5 Stepanov-Like Almost Automorphic Functions in Matched Spaces of Time Scales -- 7 Almost Periodic Dynamic Equations Under Matched Spaces -- 7.1 Basic Theory of Nonlinear Almost Periodic Dynamic Equations -- 7.2 Exponential Dichotomy of Inhomogeneous Dynamic Equations -- 7.3 δ-Almost Periodic Solutions of Dynamic Equations -- 7.4 n0-Order Δ-Almost Periodic Solutions for Dynamic Equations -- 8 Almost Automorphic Dynamic Equations Under Matched Spaces -- 8.1 Weighted Pseudo δ-Almost Automorphic Solutions for Dynamic Equations -- 8.2 n0-Order Weighted Pseudo Δ-Almost Automorphic Solutions for Dynamic Equations -- 8.3 Almost Automorphic Impulsive Dynamic Equations Based on Shift Operators -- 9 Applications to Dynamics Models Under Matched Spaces -- 9.1 Almost Periodic Neutral Impulsive Stochastic Lasota-Wazewska Timescale Model -- 9.1.1 Introduction and Model Description -- 9.1.2 Inverse Representation of the Neutral Term with Shift Operator -- 9.1.3 Existence of Mean-Square Almost Periodic Solution -- 9.2 Almost Periodic Impulsive Stochastic Nicholson's Blowflies Timescale Model -- 9.2.1 Model Description -- 9.2.2 Almost Periodic Stochastic Process Under Periodic Time Scales with Shifts δ -- 9.2.3 Mean-Square Positive Almost Periodic Solutions to the Model with Shift Operators -- 9.3 A Numerical Example and the Model on the Quantum Time Scale -- References -- Index. |
| Record Nr. | UNISA-996490344203316 |
|
Zhao Bingxuan
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Measure theory and integration / / by Ammar Khanfer
| Measure theory and integration / / by Ammar Khanfer |
| Autore | Khanfer Ammar |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore, , [2023] |
| Descrizione fisica | 1 online resource (237 pages) |
| Disciplina | 515.42 |
| Soggetto topico |
Measure theory
Measure and Integration Teoria de la mesura Mesura, Teoria de la |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789819928828
981-9928-82-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1. Measure Theory -- Chapter 2. Measurable Functions -- Chapter 3. Lebesgue Integration -- Chapter 4. Lebesgue Spaces -- Chapter 5. Abstract Measure Theory. |
| Record Nr. | UNINA-9910746095703321 |
|
Khanfer Ammar
|
||
| Singapore : , : Springer Nature Singapore, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Measure theory, probability, and stochastic processes / / Jean-François Le Gall
| Measure theory, probability, and stochastic processes / / Jean-François Le Gall |
| Autore | Le Gall J. F (Jean-François) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (409 pages) |
| Disciplina | 515.42 |
| Collana | Graduate texts in mathematics |
| Soggetto topico |
Measure theory
Probabilities Stochastic processes Teoria de la mesura Probabilitats Processos estocàstics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031142055
9783031142048 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- Part I Measure Theory -- 1 Measurable Spaces -- 1.1 Measurable Sets -- 1.2 Positive Measures -- 1.3 Measurable Functions -- Operations on Measurable Functions -- 1.4 Monotone Class -- 1.5 Exercises -- 2 Integration of Measurable Functions -- 2.1 Integration of Nonnegative Functions -- 2.2 Integrable Functions -- 2.3 Integrals Depending on a Parameter -- 2.4 Exercises -- 3 Construction of Measures -- 3.1 Outer Measures -- 3.2 Lebesgue Measure -- 3.3 Relation with Riemann Integrals -- 3.4 A Subset of ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Which Is Not Measurable -- 3.5 Finite Measures on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and the Stieltjes Integral -- 3.6 The Riesz-Markov-Kakutani Representation Theorem -- 3.7 Exercises -- 4 Lp Spaces -- 4.1 Definitions and the Hölder Inequality -- 4.2 The Banach Space ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper L Superscript p Baseline left parenthesis upper E comma script upper A comma mu right parenthesis) /StPNE pdfmark [/StBMC pdfmarkLp(E,A,μ)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 4.3 Density Theorems in Lp Spaces -- 4.4 The Radon-Nikodym Theorem -- 4.5 Exercises -- 5 Product Measures -- 5.1 Product σ-Fields -- 5.2 Product Measures -- 5.3 The Fubini Theorems -- 5.4 Applications -- 5.4.1 Integration by Parts -- 5.4.2 Convolution -- 5.4.3 The Volume of the Unit Ball -- 5.5 Exercises -- 6 Signed Measures -- 6.1 Definition and Total Variation -- 6.2 The Jordan Decomposition -- 6.3 The Duality Between Lp and Lq -- 6.4 The Riesz-Markov-Kakutani Representation Theorem for Signed Measures -- 6.5 Exercises.
7 Change of Variables -- 7.1 The Change of Variables Formula -- 7.2 The Gamma Function -- 7.3 Lebesgue Measure on the Unit Sphere -- 7.4 Exercises -- Part II Probability Theory -- 8 Foundations of Probability Theory -- 8.1 General Definitions -- 8.1.1 Probability Spaces -- 8.1.2 Random Variables -- 8.1.3 Mathematical Expectation -- 8.1.4 An Example: Bertrand's Paradox -- 8.1.5 Classical Laws -- 8.1.6 Distribution Function of a Real Random Variable -- 8.1.7 The σ-Field Generated by a Random Variable -- 8.2 Moments of Random Variables -- 8.2.1 Moments and Variance -- 8.2.2 Linear Regression -- 8.2.3 Characteristic Functions -- 8.2.4 Laplace Transform and Generating Functions -- 8.3 Exercises -- 9 Independence -- 9.1 Independent Events -- 9.2 Independence for σ-Fields and Random Variables -- 9.3 The Borel-Cantelli Lemma -- 9.4 Construction of Independent Sequences -- 9.5 Sums of Independent Random Variables -- 9.6 Convolution Semigroups -- 9.7 The Poisson Process -- 9.8 Exercises -- 10 Convergence of Random Variables -- 10.1 The Different Notions of Convergence -- 10.2 The Strong Law of Large Numbers -- 10.3 Convergence in Distribution -- 10.4 Two Applications -- 10.4.1 The Convergence of Empirical Measures -- 10.4.2 The Central Limit Theorem -- 10.4.3 The Multidimensional Central Limit Theorem -- 10.5 Exercises -- 11 Conditioning -- 11.1 Discrete Conditioning -- 11.2 The Definition of Conditional Expectation -- 11.2.1 Integrable Random Variables -- 11.2.2 Nonnegative Random Variables -- 11.2.3 The Special Case of Square Integrable Variables -- 11.3 Specific Properties of the Conditional Expectation -- 11.4 Evaluation of Conditional Expectation -- 11.4.1 Discrete Conditioning -- 11.4.2 Random Variables with a Density -- 11.4.3 Gaussian Conditioning -- 11.5 Transition Probabilities and Conditional Distributions -- 11.6 Exercises. Part III Stochastic Processes -- 12 Theory of Martingales -- 12.1 Definitions and Examples -- 12.2 Stopping Times -- 12.3 Almost Sure Convergence of Martingales -- 12.4 Convergence in Lp When p> -- 1 -- 12.5 Uniform Integrability and Martingales -- 12.6 Optional Stopping Theorems -- 12.7 Backward Martingales -- 12.8 Exercises -- 13 Markov Chains -- 13.1 Definitions and First Properties -- 13.2 A Few Examples -- 13.2.1 Independent Random Variables -- 13.2.2 Random Walks on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper Z Superscript d) /StPNE pdfmark [/StBMC pdfmarkZdps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 13.2.3 Simple Random Walk on a Graph -- 13.2.4 Galton-Watson Branching Processes -- 13.3 The Canonical Markov Chain -- 13.4 The Classification of States -- 13.5 Invariant Measures -- 13.6 Ergodic Theorems -- 13.7 Martingales and Markov Chains -- 13.8 Exercises -- 14 Brownian Motion -- 14.1 Brownian Motion as a Limit of Random Walks -- 14.2 The Construction of Brownian Motion -- 14.3 The Wiener Measure -- 14.4 First Properties of Brownian Motion -- 14.5 The Strong Markov Property -- 14.6 Harmonic Functions and the Dirichlet Problem -- 14.7 Harmonic Functions and Brownian Motion -- 14.8 Exercises -- A A Few Facts from Functional Analysis -- Normed Linear Spaces and Banach Spaces -- Hilbert Spaces -- Notes and Suggestions for Further Reading -- References -- Index. |
| Record Nr. | UNINA-9910624396803321 |
|
Le Gall J. F (Jean-François)
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Measure theory, probability, and stochastic processes / / Jean-François Le Gall
| Measure theory, probability, and stochastic processes / / Jean-François Le Gall |
| Autore | Le Gall J. F (Jean-François) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (409 pages) |
| Disciplina | 515.42 |
| Collana | Graduate texts in mathematics |
| Soggetto topico |
Measure theory
Probabilities Stochastic processes Teoria de la mesura Probabilitats Processos estocàstics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031142055
9783031142048 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- Part I Measure Theory -- 1 Measurable Spaces -- 1.1 Measurable Sets -- 1.2 Positive Measures -- 1.3 Measurable Functions -- Operations on Measurable Functions -- 1.4 Monotone Class -- 1.5 Exercises -- 2 Integration of Measurable Functions -- 2.1 Integration of Nonnegative Functions -- 2.2 Integrable Functions -- 2.3 Integrals Depending on a Parameter -- 2.4 Exercises -- 3 Construction of Measures -- 3.1 Outer Measures -- 3.2 Lebesgue Measure -- 3.3 Relation with Riemann Integrals -- 3.4 A Subset of ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Which Is Not Measurable -- 3.5 Finite Measures on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and the Stieltjes Integral -- 3.6 The Riesz-Markov-Kakutani Representation Theorem -- 3.7 Exercises -- 4 Lp Spaces -- 4.1 Definitions and the Hölder Inequality -- 4.2 The Banach Space ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper L Superscript p Baseline left parenthesis upper E comma script upper A comma mu right parenthesis) /StPNE pdfmark [/StBMC pdfmarkLp(E,A,μ)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 4.3 Density Theorems in Lp Spaces -- 4.4 The Radon-Nikodym Theorem -- 4.5 Exercises -- 5 Product Measures -- 5.1 Product σ-Fields -- 5.2 Product Measures -- 5.3 The Fubini Theorems -- 5.4 Applications -- 5.4.1 Integration by Parts -- 5.4.2 Convolution -- 5.4.3 The Volume of the Unit Ball -- 5.5 Exercises -- 6 Signed Measures -- 6.1 Definition and Total Variation -- 6.2 The Jordan Decomposition -- 6.3 The Duality Between Lp and Lq -- 6.4 The Riesz-Markov-Kakutani Representation Theorem for Signed Measures -- 6.5 Exercises.
7 Change of Variables -- 7.1 The Change of Variables Formula -- 7.2 The Gamma Function -- 7.3 Lebesgue Measure on the Unit Sphere -- 7.4 Exercises -- Part II Probability Theory -- 8 Foundations of Probability Theory -- 8.1 General Definitions -- 8.1.1 Probability Spaces -- 8.1.2 Random Variables -- 8.1.3 Mathematical Expectation -- 8.1.4 An Example: Bertrand's Paradox -- 8.1.5 Classical Laws -- 8.1.6 Distribution Function of a Real Random Variable -- 8.1.7 The σ-Field Generated by a Random Variable -- 8.2 Moments of Random Variables -- 8.2.1 Moments and Variance -- 8.2.2 Linear Regression -- 8.2.3 Characteristic Functions -- 8.2.4 Laplace Transform and Generating Functions -- 8.3 Exercises -- 9 Independence -- 9.1 Independent Events -- 9.2 Independence for σ-Fields and Random Variables -- 9.3 The Borel-Cantelli Lemma -- 9.4 Construction of Independent Sequences -- 9.5 Sums of Independent Random Variables -- 9.6 Convolution Semigroups -- 9.7 The Poisson Process -- 9.8 Exercises -- 10 Convergence of Random Variables -- 10.1 The Different Notions of Convergence -- 10.2 The Strong Law of Large Numbers -- 10.3 Convergence in Distribution -- 10.4 Two Applications -- 10.4.1 The Convergence of Empirical Measures -- 10.4.2 The Central Limit Theorem -- 10.4.3 The Multidimensional Central Limit Theorem -- 10.5 Exercises -- 11 Conditioning -- 11.1 Discrete Conditioning -- 11.2 The Definition of Conditional Expectation -- 11.2.1 Integrable Random Variables -- 11.2.2 Nonnegative Random Variables -- 11.2.3 The Special Case of Square Integrable Variables -- 11.3 Specific Properties of the Conditional Expectation -- 11.4 Evaluation of Conditional Expectation -- 11.4.1 Discrete Conditioning -- 11.4.2 Random Variables with a Density -- 11.4.3 Gaussian Conditioning -- 11.5 Transition Probabilities and Conditional Distributions -- 11.6 Exercises. Part III Stochastic Processes -- 12 Theory of Martingales -- 12.1 Definitions and Examples -- 12.2 Stopping Times -- 12.3 Almost Sure Convergence of Martingales -- 12.4 Convergence in Lp When p> -- 1 -- 12.5 Uniform Integrability and Martingales -- 12.6 Optional Stopping Theorems -- 12.7 Backward Martingales -- 12.8 Exercises -- 13 Markov Chains -- 13.1 Definitions and First Properties -- 13.2 A Few Examples -- 13.2.1 Independent Random Variables -- 13.2.2 Random Walks on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper Z Superscript d) /StPNE pdfmark [/StBMC pdfmarkZdps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 13.2.3 Simple Random Walk on a Graph -- 13.2.4 Galton-Watson Branching Processes -- 13.3 The Canonical Markov Chain -- 13.4 The Classification of States -- 13.5 Invariant Measures -- 13.6 Ergodic Theorems -- 13.7 Martingales and Markov Chains -- 13.8 Exercises -- 14 Brownian Motion -- 14.1 Brownian Motion as a Limit of Random Walks -- 14.2 The Construction of Brownian Motion -- 14.3 The Wiener Measure -- 14.4 First Properties of Brownian Motion -- 14.5 The Strong Markov Property -- 14.6 Harmonic Functions and the Dirichlet Problem -- 14.7 Harmonic Functions and Brownian Motion -- 14.8 Exercises -- A A Few Facts from Functional Analysis -- Normed Linear Spaces and Banach Spaces -- Hilbert Spaces -- Notes and Suggestions for Further Reading -- References -- Index. |
| Record Nr. | UNISA-996495167103316 |
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Le Gall J. F (Jean-François)
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum
| Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum |
| Autore | Shum Kenneth |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023 |
| Descrizione fisica | 1 online resource (262 pages) |
| Disciplina | 519.2 |
| Collana | Compact Textbooks in Mathematics |
| Soggetto topico |
Probabilities
Measure theory Probability Theory Applied Probability Measure and Integration Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-49830-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Beyond discrete and continuous random variables -- Probability spaces -- Lebesgue–Stieltjes measures -- Measurable functions and random variables -- Statistical independence -- Lebesgue integral and mathematical expectation -- Properties of Lebesgue integral and convergence theorems -- Product space and coupling -- Moment generating functions and characteristic functions -- Modes of convergence -- Laws of large numbers -- Techniques from Hilbert space theory -- Conditional expectation -- Levy’s continuity theorem and central limit theorem -- References -- Index. |
| Record Nr. | UNINA-9910835058303321 |
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Shum Kenneth
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Notes on Real Analysis and Measure Theory [[electronic resource] ] : Fine Properties of Real Sets and Functions / / by Alexander Kharazishvili
| Notes on Real Analysis and Measure Theory [[electronic resource] ] : Fine Properties of Real Sets and Functions / / by Alexander Kharazishvili |
| Autore | Kharazishvili Alexander |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (256 pages) |
| Disciplina | 515.8 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Mathematics
Funcions de variables reals Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-17033-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Real-Valued Semicontinuous Functions -- 2. The Oscillations of Real-Valued Functions -- 3. Monotone and Continuous Restrictions of Real-Valued Functions -- 4. Bijective Continuous Images of Absolute Null Sets -- 5. Projective Absolutely Nonmeasurable Functions -- 6. Borel Isomorphisms of Analytic Sets -- 7. Iterated Integrals of Real-Valued Functions of Two Real Variables -- 8. The Steinhaus Property, Ergocidity, and Density Points -- 9. Measurability Properties of H-Selectors and Partial H-Selectors -- 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets -- 11. Negligible Sets Versus Absolutely Nonmeasurable Sets -- 12. Measurability Properties of Mazurkiewicz Sets -- 13. Extensions of Invariant Measures on R -- A. A Characterization of Uncountable Sets in Terms of their Self-Mappings -- B. Some Applications of Peano Type Functions -- C. Almost Rigid Mathematical Structures -- D. Some Unsolved Problems in Measure Theory -- Bibliography -- Index. |
| Record Nr. | UNISA-996490344103316 |
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Kharazishvili Alexander
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Notes on Real Analysis and Measure Theory : Fine Properties of Real Sets and Functions / / by Alexander Kharazishvili
| Notes on Real Analysis and Measure Theory : Fine Properties of Real Sets and Functions / / by Alexander Kharazishvili |
| Autore | Kharazishvili Alexander |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (256 pages) |
| Disciplina |
515.8
515.42 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Mathematics
Funcions de variables reals Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-17033-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Real-Valued Semicontinuous Functions -- 2. The Oscillations of Real-Valued Functions -- 3. Monotone and Continuous Restrictions of Real-Valued Functions -- 4. Bijective Continuous Images of Absolute Null Sets -- 5. Projective Absolutely Nonmeasurable Functions -- 6. Borel Isomorphisms of Analytic Sets -- 7. Iterated Integrals of Real-Valued Functions of Two Real Variables -- 8. The Steinhaus Property, Ergocidity, and Density Points -- 9. Measurability Properties of H-Selectors and Partial H-Selectors -- 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets -- 11. Negligible Sets Versus Absolutely Nonmeasurable Sets -- 12. Measurability Properties of Mazurkiewicz Sets -- 13. Extensions of Invariant Measures on R -- A. A Characterization of Uncountable Sets in Terms of their Self-Mappings -- B. Some Applications of Peano Type Functions -- C. Almost Rigid Mathematical Structures -- D. Some Unsolved Problems in Measure Theory -- Bibliography -- Index. |
| Record Nr. | UNINA-9910595030303321 |
|
Kharazishvili Alexander
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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