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Convolution-like structures, differential operators and diffusion processes / / Rúben Sousa, Manuel Guerra, Semyon Yakubovich
| Convolution-like structures, differential operators and diffusion processes / / Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| Autore | Sousa Rúben (Mathematician) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (269 pages) |
| Disciplina | 512.86 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Convolutions (Mathematics)
Differential operators Diffusion processes Convolucions (Matemàtica) Operadors diferencials Processos de difusió |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-05296-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation and Scope -- 1.2 Organization of the Book -- 2 Preliminaries -- 2.1 Continuous-Time Markov Processes -- 2.2 Sturm-Liouville Theory -- 2.2.1 Solutions of the Sturm-Liouville Equation -- 2.2.2 Eigenfunction Expansions -- 2.2.3 Diffusion Semigroups Generated by Sturm-Liouville Operators -- 2.2.4 Remarkable Particular Cases -- 2.3 Generalized Convolutions and Hypergroups -- 2.4 Harmonic Analysis with Respect to the Kingman Convolution -- 3 The Whittaker Convolution -- 3.1 A Special Case: The Kontorovich-Lebedev Convolution -- 3.2 The Product Formula for the Whittaker Function -- 3.3 Whittaker Translation -- 3.4 Index Whittaker Transforms -- 3.5 Whittaker Convolution of Measures -- 3.5.1 Infinitely Divisible Distributions -- 3.5.2 Lévy-Khintchine Type Representation -- 3.6 Lévy Processes with Respect to the Whittaker Convolution -- 3.6.1 Convolution Semigroups -- 3.6.2 Lévy and Gaussian Processes -- 3.6.3 Some Auxiliary Results on the Whittaker Translation -- 3.6.4 Moment Functions -- 3.6.5 Lévy-Type Characterization of the Shiryaev Process -- 3.7 Whittaker Convolution of Functions -- 3.7.1 Mapping Properties in the Spaces Lp(rα) -- 3.7.2 The Convolution Banach Algebra Lα,ν -- 3.8 Convolution-Type Integral Equations -- 4 Generalized Convolutions for Sturm-Liouville Operators -- 4.1 Known Results and Motivation -- 4.2 Laplace-Type Representation -- 4.3 The Existence Theorem for Sturm-Liouville Product Formulas -- 4.3.1 The Associated Hyperbolic Cauchy Problem -- 4.3.2 The Time-Shifted Product Formula -- 4.3.3 The Product Formula for wλ as the Limit Case -- 4.4 Sturm-Liouville Transform of Measures -- 4.5 Sturm-Liouville Convolution of Measures -- 4.5.1 Infinite Divisibility and Lévy-Khintchine Type Representation -- 4.5.2 Convolution Semigroups.
4.5.3 Additive and Lévy Processes -- 4.6 Sturm-Liouville Hypergroups -- 4.6.1 The Nondegenerate Case -- 4.6.2 The Degenerate Case: Degenerate Hypergroups of Full Support -- 4.7 Harmonic Analysis on Lp Spaces -- 4.7.1 A Family of L1 Spaces -- 4.7.2 Application to Convolution-Type Integral Equations -- 5 Convolution-Like Structures on Multidimensional Spaces -- 5.1 Convolutions Associated with Conservative Strong Feller Semigroups -- 5.2 Nonexistence of Convolutions: Diffusion Processes on Bounded Domains -- 5.2.1 Special Cases and Numerical Examples -- 5.2.2 Some Auxiliary Results -- 5.2.3 Eigenfunction Expansions, Critical Points and Nonexistence Theorems -- 5.3 Nonexistence of Convolutions: One-Dimensional Diffusions -- 5.4 Families of Convolutions on Riemannian Structures with Cone-Like Metrics -- 5.4.1 The Eigenfunction Expansion of the Laplace-Beltrami Operator -- 5.4.2 Product Formulas and Convolutions -- 5.4.3 Infinitely Divisible Measures and Convolution Semigroups -- 5.4.4 Special Cases -- 5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2 -- A Some Open Problems -- References -- Index. |
| Record Nr. | UNISA-996483172603316 |
Sousa Rúben (Mathematician)
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Convolution-like structures, differential operators and diffusion processes / / Rúben Sousa, Manuel Guerra, Semyon Yakubovich
| Convolution-like structures, differential operators and diffusion processes / / Rúben Sousa, Manuel Guerra, Semyon Yakubovich |
| Autore | Sousa Rúben (Mathematician) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (269 pages) |
| Disciplina | 512.86 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Convolutions (Mathematics)
Differential operators Diffusion processes Convolucions (Matemàtica) Operadors diferencials Processos de difusió |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-05296-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation and Scope -- 1.2 Organization of the Book -- 2 Preliminaries -- 2.1 Continuous-Time Markov Processes -- 2.2 Sturm-Liouville Theory -- 2.2.1 Solutions of the Sturm-Liouville Equation -- 2.2.2 Eigenfunction Expansions -- 2.2.3 Diffusion Semigroups Generated by Sturm-Liouville Operators -- 2.2.4 Remarkable Particular Cases -- 2.3 Generalized Convolutions and Hypergroups -- 2.4 Harmonic Analysis with Respect to the Kingman Convolution -- 3 The Whittaker Convolution -- 3.1 A Special Case: The Kontorovich-Lebedev Convolution -- 3.2 The Product Formula for the Whittaker Function -- 3.3 Whittaker Translation -- 3.4 Index Whittaker Transforms -- 3.5 Whittaker Convolution of Measures -- 3.5.1 Infinitely Divisible Distributions -- 3.5.2 Lévy-Khintchine Type Representation -- 3.6 Lévy Processes with Respect to the Whittaker Convolution -- 3.6.1 Convolution Semigroups -- 3.6.2 Lévy and Gaussian Processes -- 3.6.3 Some Auxiliary Results on the Whittaker Translation -- 3.6.4 Moment Functions -- 3.6.5 Lévy-Type Characterization of the Shiryaev Process -- 3.7 Whittaker Convolution of Functions -- 3.7.1 Mapping Properties in the Spaces Lp(rα) -- 3.7.2 The Convolution Banach Algebra Lα,ν -- 3.8 Convolution-Type Integral Equations -- 4 Generalized Convolutions for Sturm-Liouville Operators -- 4.1 Known Results and Motivation -- 4.2 Laplace-Type Representation -- 4.3 The Existence Theorem for Sturm-Liouville Product Formulas -- 4.3.1 The Associated Hyperbolic Cauchy Problem -- 4.3.2 The Time-Shifted Product Formula -- 4.3.3 The Product Formula for wλ as the Limit Case -- 4.4 Sturm-Liouville Transform of Measures -- 4.5 Sturm-Liouville Convolution of Measures -- 4.5.1 Infinite Divisibility and Lévy-Khintchine Type Representation -- 4.5.2 Convolution Semigroups.
4.5.3 Additive and Lévy Processes -- 4.6 Sturm-Liouville Hypergroups -- 4.6.1 The Nondegenerate Case -- 4.6.2 The Degenerate Case: Degenerate Hypergroups of Full Support -- 4.7 Harmonic Analysis on Lp Spaces -- 4.7.1 A Family of L1 Spaces -- 4.7.2 Application to Convolution-Type Integral Equations -- 5 Convolution-Like Structures on Multidimensional Spaces -- 5.1 Convolutions Associated with Conservative Strong Feller Semigroups -- 5.2 Nonexistence of Convolutions: Diffusion Processes on Bounded Domains -- 5.2.1 Special Cases and Numerical Examples -- 5.2.2 Some Auxiliary Results -- 5.2.3 Eigenfunction Expansions, Critical Points and Nonexistence Theorems -- 5.3 Nonexistence of Convolutions: One-Dimensional Diffusions -- 5.4 Families of Convolutions on Riemannian Structures with Cone-Like Metrics -- 5.4.1 The Eigenfunction Expansion of the Laplace-Beltrami Operator -- 5.4.2 Product Formulas and Convolutions -- 5.4.3 Infinitely Divisible Measures and Convolution Semigroups -- 5.4.4 Special Cases -- 5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2 -- A Some Open Problems -- References -- Index. |
| Record Nr. | UNINA-9910585774303321 |
|
Sousa Rúben (Mathematician)
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Functional analytic techniques for diffusion processes / / Kazuaki Taira
| Functional analytic techniques for diffusion processes / / Kazuaki Taira |
| Autore | Taira Kazuaki |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (792 pages) |
| Disciplina | 519.233 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Diffusion processes
Markov processes Processos de difusió |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811910999
9789811910982 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996479372403316 |
|
Taira Kazuaki
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Functional analytic techniques for diffusion processes / / Kazuaki Taira
| Functional analytic techniques for diffusion processes / / Kazuaki Taira |
| Autore | Taira Kazuaki |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (792 pages) |
| Disciplina | 519.233 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Diffusion processes
Markov processes Processos de difusió |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811910999
9789811910982 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910574083003321 |
|
Taira Kazuaki
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random walk and diffusion models : an introduction for life and behavioral scientists / / Wolf Schwarz
| Random walk and diffusion models : an introduction for life and behavioral scientists / / Wolf Schwarz |
| Autore | Schwarz Wolf |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (218 pages) |
| Disciplina | 570.15195 |
| Soggetto topico |
Diffusion processes
Biomatemàtica Processos de difusió Rutes aleatòries (Matemàtica) Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031121005
9783031120992 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Random Walk and Diffusion Models in the Life and the Behavioral Sciences -- 1.2 Two Historic Examples -- 1.2.1 Galton's Board -- 1.2.2 The Laws of Fick and the Diffusion of Substance -- 1.3 Exercises -- 2 Discrete Random Walks -- 2.1 The Symmetric Simple Random Walk -- 2.1.1 Unrestricted Evolution: Some Basic Properties -- 2.2 The Simple Random Walk with Drift -- 2.2.1 Unrestricted Evolution: Some Basic Properties -- 2.2.2 The Forward and the Backward Equation -- 2.3 Discrete Random Walks in the Presence of Barriers -- 2.3.1 Absorption Probability with a Single Barrier -- 2.3.2 Absorption Probability with Two Barriers -- 2.3.3 Mean First-Passage Time to a Single Barrier -- 2.3.4 Mean First-Passage Time with Two Barriers -- 2.3.5 Conditional Mean First-Passage Time with Two Barriers -- 2.3.6 Generating Functions for First-Passage Problems -- 2.4 The Correlated Random Walk -- 2.4.1 Unrestricted Evolution: The Basic Transition Matrix -- 2.4.2 The Mean and Variance of Correlated Random Walks -- 2.4.3 Correlated Random Walks Between Absorbing Barriers -- 2.4.4 Correlated Random Walks with Randomized Initial Directional State -- 2.5 More General Random Walks -- 2.5.1 The Ehrenfest Model -- 2.5.2 The Fisher-Wright Model of Random Genetic Drift -- 2.6 Exercises -- 3 Small Steps at High Speed: The Diffusion Limit -- 3.1 Small Steps at High Speed: The Diffusion Limit -- 3.2 The Diffusion Equation -- 3.2.1 From Difference Equations to Differential Equations -- 3.2.2 Fick's Laws, Galton's Board, and the Diffusion Equation -- 3.3 An Alternative Derivation: The Moment-Generating Function -- 3.4 Some Elementary Properties of the Continuous Limit -- 3.5 Exercises -- 4 Diffusion with Drift: The Wiener Process -- 4.1 Unrestricted Evolution -- 4.1.1 Limit Conditions for Discrete Random Walks with Drift.
4.1.2 The Forward Equation in the Presence of Drift -- 4.1.3 The Backward Equation for the Wiener Process -- 4.1.4 Explicit Form of the Transition Density -- 4.2 One Absorbing Barrier -- 4.2.1 The Forward Equation for First-Passage Times -- 4.2.2 The Backward Equation for First-Passage Times -- 4.2.3 An Alternative Derivation: The Moment-Generating Function -- 4.3 One Reflecting Barrier -- 4.3.1 Reflecting Barrier in the Absence of Drift -- 4.3.2 Reflecting Barrier in the Presence of Drift -- 4.4 Two Absorbing Barriers -- 4.4.1 Absorption Probability -- 4.4.2 Mean First-Passage Times -- 4.4.3 First-Passage Time Distributions -- 4.4.4 Moment-Generating Functions for Two Barriers -- 4.5 Two Reflecting Barriers -- 4.6 The Mixed Case: One Absorbing and One Reflecting Barrier -- 4.7 The Backward Process -- 4.8 Exercises -- 5 More General Diffusion Processes -- 5.1 Diffusion Processes with State-Dependent Drift and Variance -- 5.2 The Generalized Forward and Backward Diffusion Equations -- 5.3 Examples of More General Diffusion Processes -- 5.3.1 The Ornstein-Uhlenbeck (OU) Process -- 5.3.2 The Fisher-Wright Process -- 5.4 Siegert's Equation for First-Passage Times -- 5.4.1 Application of Siegert's Equation to the Wiener Process -- 5.5 The Darling and Siegert Equations -- 5.6 Exercises -- 6 Differential Equations for Probabilities and Means -- 6.1 Introduction -- 6.2 Two Absorbing Barriers: Unconditional Results -- 6.2.1 Boundary Conditions and Explicit Solutions -- 6.2.2 Mean Unconditional First-Passage Time -- 6.2.3 Examples -- 6.3 Two Absorbing Barriers: Conditional Results -- 6.3.1 Boundary Conditions and Solutions -- 6.3.2 Absorption Probabilities -- 6.3.3 Mean Conditional First-Passage Time -- 6.3.4 Boundary Conditions for the Conditional Case -- 6.3.5 Examples -- 6.4 One Absorbing and One Reflecting Barrier -- 6.4.1 Boundary Conditions and Solutions. 6.4.2 Mean First-Passage Times -- 6.5 Exercises -- 7 Applications of Random Walk and Diffusion Models in the Life and Behavioral Sciences -- 7.1 Stephen J. Gould: The Spread of Excellence -- 7.2 Modeling First Hitting Times -- 7.3 Correlated Random Walks: Generalizations and Applications -- 7.4 Random Walk and Diffusion Models of Animal Movement -- 7.5 Random Walk and Diffusion Models in Sports -- 7.6 Random Walk and Diffusion Models of Animal Decision-Making -- 7.6.1 Sequential Sampling Models of Neuronal Activity in Perceptual Decision-Making -- 7.6.2 Random Walk Models of Discrimination and Choice Behavior in Animals -- 7.6.3 Random Walk Models of Group Decision-Making in Animals -- 7.7 Random Walk and Diffusion Models of Human Decision-Making -- 7.8 Some Further Applications of Random Walk and Diffusion Models in the Behavioral and Life Sciences -- 7.9 Exercises -- References -- I. Books -- II. Articles -- Index. |
| Record Nr. | UNINA-9910616380203321 |
|
Schwarz Wolf
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random walk and diffusion models : an introduction for life and behavioral scientists / / Wolf Schwarz
| Random walk and diffusion models : an introduction for life and behavioral scientists / / Wolf Schwarz |
| Autore | Schwarz Wolf |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (218 pages) |
| Disciplina | 570.15195 |
| Soggetto topico |
Diffusion processes
Biomatemàtica Processos de difusió Rutes aleatòries (Matemàtica) Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031121005
9783031120992 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Random Walk and Diffusion Models in the Life and the Behavioral Sciences -- 1.2 Two Historic Examples -- 1.2.1 Galton's Board -- 1.2.2 The Laws of Fick and the Diffusion of Substance -- 1.3 Exercises -- 2 Discrete Random Walks -- 2.1 The Symmetric Simple Random Walk -- 2.1.1 Unrestricted Evolution: Some Basic Properties -- 2.2 The Simple Random Walk with Drift -- 2.2.1 Unrestricted Evolution: Some Basic Properties -- 2.2.2 The Forward and the Backward Equation -- 2.3 Discrete Random Walks in the Presence of Barriers -- 2.3.1 Absorption Probability with a Single Barrier -- 2.3.2 Absorption Probability with Two Barriers -- 2.3.3 Mean First-Passage Time to a Single Barrier -- 2.3.4 Mean First-Passage Time with Two Barriers -- 2.3.5 Conditional Mean First-Passage Time with Two Barriers -- 2.3.6 Generating Functions for First-Passage Problems -- 2.4 The Correlated Random Walk -- 2.4.1 Unrestricted Evolution: The Basic Transition Matrix -- 2.4.2 The Mean and Variance of Correlated Random Walks -- 2.4.3 Correlated Random Walks Between Absorbing Barriers -- 2.4.4 Correlated Random Walks with Randomized Initial Directional State -- 2.5 More General Random Walks -- 2.5.1 The Ehrenfest Model -- 2.5.2 The Fisher-Wright Model of Random Genetic Drift -- 2.6 Exercises -- 3 Small Steps at High Speed: The Diffusion Limit -- 3.1 Small Steps at High Speed: The Diffusion Limit -- 3.2 The Diffusion Equation -- 3.2.1 From Difference Equations to Differential Equations -- 3.2.2 Fick's Laws, Galton's Board, and the Diffusion Equation -- 3.3 An Alternative Derivation: The Moment-Generating Function -- 3.4 Some Elementary Properties of the Continuous Limit -- 3.5 Exercises -- 4 Diffusion with Drift: The Wiener Process -- 4.1 Unrestricted Evolution -- 4.1.1 Limit Conditions for Discrete Random Walks with Drift.
4.1.2 The Forward Equation in the Presence of Drift -- 4.1.3 The Backward Equation for the Wiener Process -- 4.1.4 Explicit Form of the Transition Density -- 4.2 One Absorbing Barrier -- 4.2.1 The Forward Equation for First-Passage Times -- 4.2.2 The Backward Equation for First-Passage Times -- 4.2.3 An Alternative Derivation: The Moment-Generating Function -- 4.3 One Reflecting Barrier -- 4.3.1 Reflecting Barrier in the Absence of Drift -- 4.3.2 Reflecting Barrier in the Presence of Drift -- 4.4 Two Absorbing Barriers -- 4.4.1 Absorption Probability -- 4.4.2 Mean First-Passage Times -- 4.4.3 First-Passage Time Distributions -- 4.4.4 Moment-Generating Functions for Two Barriers -- 4.5 Two Reflecting Barriers -- 4.6 The Mixed Case: One Absorbing and One Reflecting Barrier -- 4.7 The Backward Process -- 4.8 Exercises -- 5 More General Diffusion Processes -- 5.1 Diffusion Processes with State-Dependent Drift and Variance -- 5.2 The Generalized Forward and Backward Diffusion Equations -- 5.3 Examples of More General Diffusion Processes -- 5.3.1 The Ornstein-Uhlenbeck (OU) Process -- 5.3.2 The Fisher-Wright Process -- 5.4 Siegert's Equation for First-Passage Times -- 5.4.1 Application of Siegert's Equation to the Wiener Process -- 5.5 The Darling and Siegert Equations -- 5.6 Exercises -- 6 Differential Equations for Probabilities and Means -- 6.1 Introduction -- 6.2 Two Absorbing Barriers: Unconditional Results -- 6.2.1 Boundary Conditions and Explicit Solutions -- 6.2.2 Mean Unconditional First-Passage Time -- 6.2.3 Examples -- 6.3 Two Absorbing Barriers: Conditional Results -- 6.3.1 Boundary Conditions and Solutions -- 6.3.2 Absorption Probabilities -- 6.3.3 Mean Conditional First-Passage Time -- 6.3.4 Boundary Conditions for the Conditional Case -- 6.3.5 Examples -- 6.4 One Absorbing and One Reflecting Barrier -- 6.4.1 Boundary Conditions and Solutions. 6.4.2 Mean First-Passage Times -- 6.5 Exercises -- 7 Applications of Random Walk and Diffusion Models in the Life and Behavioral Sciences -- 7.1 Stephen J. Gould: The Spread of Excellence -- 7.2 Modeling First Hitting Times -- 7.3 Correlated Random Walks: Generalizations and Applications -- 7.4 Random Walk and Diffusion Models of Animal Movement -- 7.5 Random Walk and Diffusion Models in Sports -- 7.6 Random Walk and Diffusion Models of Animal Decision-Making -- 7.6.1 Sequential Sampling Models of Neuronal Activity in Perceptual Decision-Making -- 7.6.2 Random Walk Models of Discrimination and Choice Behavior in Animals -- 7.6.3 Random Walk Models of Group Decision-Making in Animals -- 7.7 Random Walk and Diffusion Models of Human Decision-Making -- 7.8 Some Further Applications of Random Walk and Diffusion Models in the Behavioral and Life Sciences -- 7.9 Exercises -- References -- I. Books -- II. Articles -- Index. |
| Record Nr. | UNISA-996495170903316 |
|
Schwarz Wolf
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
