Probability and Stochastic Processes

Preface

This book originated as a series of lecture notes for a first year graduate class taught during two semesters at Stevens Institute of Technology. It covers probability, which is taught during the first semester, and stochastic processes, taught in the second semester. Thus the book is structured to cover both subject in a wide enough manner to allow applications to many domains.

Probability is an old subject. Stochastic processes is a new subject that is quickly becoming old. So why write a book on an old subject? In my opinion, this book is necessary at the current day and age. The fundamental textbooks are becoming too complex for the new students and, in an effort to make the material more accessible to students, new applied probability books discard the rigor of the old books and the painstaking details that is put forward in these old textbooks. At times, reading these new books feels like the authors are inventing new notions to be able to skip the old reasoning. I believe that this is not needed. I believe that it is possible to have a mathematically rigorous textbook which is at the same time accessible to students. The result is this work. This book does not try to reinvent the concepts only to put them into an accessible format. Throughout, I have tried to explain complex notions with as many details as possible. For this reason to a versed reader in the subject, many of the derivations will seem to contain unnecessary details. Let me assure you that for a ...