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Stochastic calculus and stochastic models /
Stochastic Calculus and Stochastic Models.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1974.
|
| Colección: | Probability and mathematical statistics ;
25. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Stochastic Calculus and Stochastic Models; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter I. Introduction; 0 Motivation, and a Forward Look; 1 Random Variables; 2 Conditional Expectations; 3 Stochastic Processes; Chapter II. Stochastic Integrals; 1 Stochastic Models and Properties They Should Possess; 2 Definition of the Integral; 3 The Canonical Form; 4 Elementary Properties of the Integral; 5 The It�o-Belated Integral; Chapter III. Existence of Stochastic Integrals; 1 Fundamental Lemma; 2 Existence of the Stochastic Integral: First Theorem.
- 3 Second Existence Theorem4 Third and Fourth Existence Theorems; 5 The Vanishing of Certain Integrals; 6 Special Cases; 7 Examples: Brownian Motions; Point Processes; 8 Extension to the It�o-Belated Integral; Chapter IV. Continuity, Chain Rule, and Substitution; 1 Continuity of Sample Functions; 2 Differentiation of a Composite Function; 3 Applications of It�o's Differentiation Formula; 4 Substitution; 5 Extension to It�o-Belated Integrals; Chapter V. Stochastic Differential Equations; 1 Existence of Solutions of Stochastic Differential Equations.
- 2 Linear Differential Equations and Their Adjoints3 An Approximation Lemma; 4 The Cauchy-Maruyama Approximation; Chapter VI. Equations in Canonical Form; 1 Invariance under Change of Coordinates; 2 Runge-Kutta Approximations; 3 Comparision of Ordinary and Stochastic Differential Equations; 4 Rate of Convergence of Approximations to Solutions; 5 Continuous Dependence of the Solution on the Disturbance; 6 Justification of the Canonical Extension in Stochastic Modeling; References; Subject Index.