Stochastic processes play a basic role in several problems of many branches of physical, biological, and social sciences, business and economics, and engineering. Having recognized the applicatory value of the theory of stochastic processes, almost all colleges and universities offer a course on this subject at least for a semester or quarter to suit the needs of students majoring in various areas.
This textbook is based on my lectures given at the University of Georgia and University of Guelph. The composition of my classes varied from year to year with students from the junior level to the first year graduate level and majors in mathematics, statistics, physics, chemistry, zoology, ecology, and business. With the exception of a couple of sections, all the material in the book has been covered at one time or another.
The book treats most of the major areas of stochastic processes. The first objective of the book is to present various techniques used in the study of stochastic processes. The notion of stopping time is introduced at a very early stage and is used throughout the book. At several places we have explained the intuition behind these techniques. The material covered in this book will prepare a student for further advanced study of stochastic processes. Our next objective is to point out the applicatory value of this area of mathematics. Almost all the topics have been motivated and illustrated by drawing exampies and applications from various branches of sciences.