Almost Periodic Stochastic Processes

Extending the author's work on almost periodic stochastic difference and differential equations, this book covers almost periodic random processes and applications. Covers existence, uniqueness, and stability of solutions for abstract stochastic difference.

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 Includes supplementary material: sn.pub/extras

Klappentext

Almost Periodic Stochastic Processes is among the few published books that is entirely devoted to almost periodic stochastic processes and their applications. The topics treated range from existence, uniqueness, boundedness, and stability of solutions, to stochastic difference and differential equations. Motivated by the studies of the natural fluctuations in nature, this work aims to lay the foundations for a theory on almost periodic stochastic processes and their applications.

This book is divided in to eight chapters and offers useful bibliographical notes at the end of each chapter. Highlights of this monograph include the introduction of the concept of p-th mean almost periodicity for stochastic processes and applications to various equations. The book offers some original results on the boundedness, stability, and existence of p-th mean almost periodic solutions to (non)autonomous first and/or second order stochastic differential equations, stochastic partial differential equations, stochastic functional differential equations with delay, and stochastic difference equations. Various illustrative examples are also discussed throughout the book.

The results provided in the book will be of particular use to those conducting research in the field of stochastic processing including engineers, economists, and statisticians with backgrounds in functional analysis and stochastic analysis. Advanced graduate students with backgrounds in real analysis, measure theory, and basic probability, may also find the material in this book quite useful and engaging.

Inhalt
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.