Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting
time varying randomness. In a lively and imaginative presentation, studded with examples, exercises, and applications,
and supported by inclusion of computational procedures, the author has created a textbook that provides easy access
to this fundamental topic for many students of applied sciences at many levels. With its carefully modularized
discussion and crystal clear differentiation between rigorous proof and plausibility argument, it is accessible
to beginners but flexible enough to serve as well those who come to the course with strong backgrounds. The prerequisite
background for reading the book is a graduate level pre-measure theoretic probability course. No knowledge of measure
theory is presumed and advanced notions of conditioning are scrupulously avoided until the later chapters of the
book.
The book can be used for either a one or two semester course as given in departments of mathematics, statistics,
operation research, business and management, or a number of engineering departments. Its approach to exercises
and applications is practical and serious. Some underlying principles of complex problems and computations are
cleanly and quickly delineated through rich vignettes of whimsically imagined Happy Harry and his Optima Street
gang�s adventures in a world whose randomness is a never-ending source of both wonder and scientific insight.
The tools of applied probability---discrete spaces, Markov chains, renewal theory, point processes, branching processes,
random walks, Brownian motion---are presented to the reader in illuminating discussion. Applications include such
topics as queuing, storage, risk analysis, genetics, inventory, choice, economics, sociology, and other. Because
of the conviction that analysts who build models should know how to build them for each class of process studied,
the author has included such constructions.
Table of Contents
1. Preliminaries: Discrete Index Sets and/or Discrete State Spaces
2. Markov Chains
3. Renewal Theory
4. Point Processes
5. Continuous Time Markov Chains
6. Brownian Motion
7. The General Random Walk
