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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->
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| ℗♭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. | UNISA-996490344203316 |
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Zhao Bingxuan
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Combined Measure and Shift Invariance Theory of Time Scales and Applications / / by Chao Wang, Ravi P. Agarwal
| Combined Measure and Shift Invariance Theory of Time Scales and Applications / / by Chao Wang, Ravi P. Agarwal |
| Autore | Zhao Bingxuan |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (443 pages) |
| Disciplina | 381 |
| Collana | Developments in Mathematics |
| Soggetto topico |
Functional analysis
Differential equations Measure theory Functions of real variables Functional Analysis Differential Equations Measure and Integration Real Functions 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 | Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales -- ♢α-Measurability and Combined Measure Theory on Time Scales -- Shift Invariance and Matched Spaces of Time Scales -- Almost Periodic Functions under Matched Spaces of Time Scales -- Almost Automorphic Functions under Matched Spaces of Time Scales -- C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales -- Almost Periodic Dynamic Equations under Matched Spaces -- Almost Automorphic Dynamic Equations under Matched Spaces -- Applications on Dynamics Models under Matched Spaces. |
| Record Nr. | UNINA-9910595037203321 |
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Zhao Bingxuan
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Decision Theory / / by Takashi Hayashi
| Decision Theory / / by Takashi Hayashi |
| Autore | Hayashi Takashi |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (0 pages) |
| Disciplina | 519.5 |
| Collana | Monographs in Mathematical Economics |
| Soggetto topico |
Mathematical statistics
Measure theory Mathematical Statistics Measure and Integration Estadística matemàtica Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
981-9522-00-5
9789819522002 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1 Preference and its representation -- Chapter 2 Revealed Preference -- Chapter 3 Choice with multiple components and separability -- Chapter 4 Decision under risk -- Chapter 5 Decision under uncertainty and subjective belief -- Chapter 6 Ambiguity of Belief -- Chapter 7 Updating belief and dynamic consistency -- Chapter 8 Intertemporal choice -- Chapter 9 Choice of opportunity -- Chapter 10 Information and Knowledge -- Chapter 11 Social decision making under uncertainty -- Chapter 12 Social decision making over time. |
| Record Nr. | UNINA-9911049082603321 |
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Hayashi Takashi
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Lectures on Optimal Transport / / by Luigi Ambrosio, Elia Brué, Daniele Semola
| Lectures on Optimal Transport / / by Luigi Ambrosio, Elia Brué, Daniele Semola |
| Autore | Ambrosio Luigi |
| Edizione | [2nd ed. 2024.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 |
| Descrizione fisica | 1 online resource (XI, 260 p. 2 illus., 1 illus. in color.) |
| Disciplina | 515 |
| Collana | La Matematica per il 3+2 |
| Soggetto topico |
Mathematical analysis
Mathematical optimization Calculus of variations Measure theory Mathematics Analysis Calculus of Variations and Optimization Measure and Integration Optimització matemàtica Teoria de la mesura |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031768347
3031768345 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | - 1. Lecture I. Preliminary notions and the Monge problem -- 2. Lecture II. The Kantorovich problem -- 3. Lecture III. The Kantorovich - Rubinstein duality -- 4. Lecture IV. Necessary and sufficient optimality conditions -- 5. Lecture V. Existence of optimal maps and applications -- 6. Lecture VI. A proof of the isoperimetric inequality and stability in Optimal Transport -- 7. Lecture VII. The Monge-Ampére equation and Optimal Transport on Riemannian manifolds -- 8. Lecture VIII. The metric side of Optimal Transport -- 9. Lecture IX. Analysis on metric spaces and the dynamic formulation of Optimal Transport -- 10. Lecture X.Wasserstein geodesics, nonbranching and curvature -- 11. Lecture XI. Gradient flows: an introduction -- 12. Lecture XII. Gradient flows: the Brézis-Komura theorem -- 13. Lecture XIII. Examples of gradient flows in PDEs -- 14. Lecture XIV. Gradient flows: the EDE and EDI formulations -- 15. Lecture XV. Semicontinuity and convexity of energies in the Wasserstein space -- 16. Lecture XVI. The Continuity Equation and the Hopf-Lax semigroup -- 17. Lecture XVII. The Benamou-Brenier formula -- 18. Lecture XVIII. An introduction to Otto’s calculus -- 19. Lecture XIX. Heat flow, Optimal Transport and Ricci curvature. |
| Record Nr. | UNINA-9910919815603321 |
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Ambrosio Luigi
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Measure and Integration : An Introduction / / by Satya N. Mukhopadhyay, Subhasis Ray
| Measure and Integration : An Introduction / / by Satya N. Mukhopadhyay, Subhasis Ray |
| Autore | Mukhopadhyay Satya N |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (647 pages) |
| Disciplina | 515.42 |
| Altri autori (Persone) | RaySubhasis |
| Collana | University Texts in the Mathematical Sciences |
| Soggetto topico |
Measure theory
Associative rings Associative algebras Functions of real variables Measure and Integration Associative Rings and Algebras Real Functions Teoria de la mesura Anells associatius Àlgebres associatives Funcions de variables reals |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 9789819725113 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Lebesgue Measure on Real Line -- Measurable Functions -- More about Sets and Functions -- The Lebesgue Integral -- Differentiation of Functions -- Lebesgue measure and integration in RN -- General Measure and Outer Measure -- Function Spaces -- Signed Measure and Complex Measure. |
| Record Nr. | UNINA-9910983484303321 |
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Mukhopadhyay Satya N
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (237 pages) |
| Disciplina | 515.42 |
| Soggetto topico |
Measure theory
Measure and Integration Teoria de la mesura |
| 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 |
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Khanfer Ammar
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Measure Theory for Analysis and Probability / / by Alok Goswami, B.V. Rao
| Measure Theory for Analysis and Probability / / by Alok Goswami, B.V. Rao |
| Autore | Goswami Alok |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (387 pages) |
| Disciplina | 515.42 |
| Altri autori (Persone) | RaoB. V |
| Collana | Indian Statistical Institute Series |
| Soggetto topico |
Measure theory
Probabilities Measure and Integration Probability Theory Teoria de la mesura Probabilitats |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789819779291
9819779294 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Measure Theory: Why and What -- 2. Measures: Construction and Properties -- 3. Measurable Functions and Integration -- 4. Random Variables and Random Vectors -- 5. Product Spaces -- 6. Radon-Nikodym Theorem and Lp Spaces -- 7. Convergence and Laws of Large Numbers -- 8. Weak convergence and Central Limit Theorem -- 9. Conditioning: The Right Approach -- 10. Infinite Products -- 11. Brownian Motion: A Brief Journey. |
| Record Nr. | UNINA-9910986138703321 |
|
Goswami Alok
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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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Soggetto topico
-
Teoria de la mesura
(17)
- Measure theory (11)
- Measure and Integration (10)
- Probabilities (7)
- Probabilitats (6)