Stochastic Functional Differential Equations (Chapman & Hall CRC Research Notes in Mathematics Series)

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Contents\0......Page 5
Preface\0......Page 7
§2. Measure and Probability\0......Page 13
§3. Vector Measures and the Dunford-Schwartz Integral\0......Page 20
§4. Some Linear Analysis\0......Page 23
§5. Stochastic Processes and Random Fields\0......Page 26
§6. Martingales\0......Page 28
§7. Markov Processes\0......Page 30
(A) Gaussian Fields\0......Page 33
(B) Brownian Motion\0......Page 34
(C) The Stochastic Integral\0......Page 36
§1. Basic Setting and Assumptions\0......Page 42
§2. Existence and Uniqueness of Solutions\0......Page 45
§3. Dependence on the Initial Process\0......Page 53
§1. The Markov Property\0......Page 58
§2. Time-Homogeneity: Autonomous Stochastic FDE\'s\0......Page 70
§3. The Semigroup\0......Page 78
§1. Notation\0......Page 82
§2. Continuity of the Semigroup\0......Page 83
§3. The Weak Infinitesimal Generator\0......Page 88
§4. Action of the Generator on Quasi-tame Functions\0......Page 109
§6. Introduction\0......Page 125
§7. Stochastic FDE\'s with Ordinary Diffusion Coefficients\0......Page 126
§8. Delayed Diffusion: An Example of Erratic Behaviour\0......Page 156
§9. Regularity in Probability for Autonomous Systems\0......Page 161
§2. Stochastic ODE\'s\0......Page 177
§3. Stochastic Delay Equations\0......Page 179
§4. Linear FDE\'s Forced by White Noise\0......Page 203
§2. A Model for Physical Brownian Motion\0......Page 235
§3. Stochastic FDE\'s with Discontinuous Initial Data\0......Page 238
§4. Stochastic Integro-Differential Equations\0......Page 240
§5. Infinite Delays\0......Page 242
REFERENCES\0......Page 246
INDEX\0......Page 252