Random walk and diffusion models : an introduction for life and behavioral scientists / / Wolf Schwarz

• Autore: Schwarz Wolf
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©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
• Nota di bibliografia: Includes bibliographical references and index.
• 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.
• Titolo autorizzato: Random Walk and Diffusion Models
• ISBN: 9783031121005; 9783031120992
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996495170903316
• Lo trovi qui: Univ. di Salerno