Preface.-1. Banach and Hilbert Spaces.-2. Bounded and Unbounded Linear Operators.- 3.An Introduction to Stochastic Differential Equations.-4. P-th Mean Almost Periodic Random Functions.-5. Existence Results for Some Stochastic Differential Equations.-6. Existence Results for Some Partial Stochastic Differential Equations.-7.Existence Results for Some Second-Order Stochastic Differential Equations.-8. Mean Almost Periodic Random Sequences and Their Applications to Stochastic Difference Equations.-References.-Index.
This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.
- This is the first book on almost periodic stochastic processes - The topics treated concern a wide audience including mathematicians, statisticians, engineers, and economists - Advanced graduate students with backgrounds in functional analysis and stochastic analysis may also find the material in this book useful