Stochastic Functional Differential Equations (Research Notes in Mathematics, Vol. 99)

✍ Scribed by S. E. A. Mohammed

• Publisher: Pitman Advanced Pub. Program
• Year: 1984
• Tongue: English
• Leaves: 257
• Edition: 1
• Category: Library

✦ Table of Contents

Cover
Title Page
Copyright Page
Dedication
Contents
Preface
I. PRELIMINARY BACKGROUND
§1. Introduction
§2. Measure and Probability
§3. Vector Measures and the Dunford-Schwartz Integral
§4. Some Linear Analysis
§5. Stochastic Processes and Random Fields
§6. Martingales
§7. Markov Processes
§8. Examples
(A) Gaussian Fields
(B) Brownian Motion
(C) The Stochastic Integral
II. EXISTENCE OF SOLUTIONS AND DEPENDENCE ON THE INITIAL PROCESS
§1. Basic Setting and Assumptions
§2. Existence and Uniqueness of Solutions
§3. Dependence on the Initial Process
III.MARKOV TRAJECTORIES
§1. The Markov Property
§2. Time-Homogeneity: Autonomous Stochastic FDE's
§3. The Semigroup
IV. THE INFINITESIMAL GENERATOR
§1. Notation
§2. Continuity of the Semigroup
§3. The Weak Infinitesimal Generator
§4. Action of the Generator on Quasi-tame Functions
§5. REGULARITY OF THE TRAJECTORY FIELD
§6. Introduction
§7. Stochastic FDE's with Ordinary Diffusion Coefficients
§8. Delayed Diffusion: An Example of Erratic Behaviour
§9. Regularity in Probability for Autonomous Systems
VI. EXAMPLES
§1. Introduction
§2. Stochastic ODE's
§3. Stochastic Delay Equations
§4. Linear FDE's Forced by White Noise
VII. FURTHER DEVELOPMENTS, PROBLEMS AND CONJECTURES
§1. Introduction
§2. A Model for Physical Brownian Motion
§3. Stochastic FDE's with Discontinuous Initial Data
§4. Stochastic Integro-Differential Equations
§5. Infinite Delays
REFERENCES
INDEX