Introduction to Stochastic Processes

This book is a follow-up to our previous book ‘Fundamentals of Probability Theory’ published in November, 2016 and it is meant for advanced undergradu- ate level and graduate level students with basic knowledge in probability; also, young researchers in other disciplines who want to brush-up their knowledge in stochastic processes may find this book useful. Theory of Stochastic Processes is one of the major and most important offshoots of Probability Theory. It is a very rich subject with applications in various branches of science, like Physics, Chemistry, Biology, Engineering and others, and of social science, like Economics, Finance etc. It is an universal truth that nothing remains constant in this world, but changes with time; and from the modern view-point, these changes are never deterministic but influenced by numerous chance factors, and hence, random in nature, governed by some probability distribution. In other words, they are all, in some form or other, stochastic processes. So for the scientific study of any phenomenon in this real world, theory of stochastic processes offers the only recourse to rely on. Thus, a sound understanding of this theory is of paramount importance. In this book, we have tried to introduce the reader to the elegance of this theory and to the immense possibilities it opens up. The reader is assumed to be familiar with basic theory of modern probability, for which our previous book may prove handy. Describes The Main Features Of Major Stochastic Processes, Giving Definition Of Basic Concepts And Presenting Key Results With Rigorous Proofs. The Theory Is Developed From Basic Foundation With A View To Build A Sound Understanding Of The Subject. An Introduction To Ergodic Theory Is Presented In The Second Part Of The Book. Cover 1 Title page 2 copyright 3 Preface 6 Contents 14 PART I 18 PART II 487 Bibliography 582 Index 591