Elements of Stochastic Processes: A Computational Approach

This book is a one-semester upper-level undergraduate treatment of some of the fundamental probabilistic models that arise in many diverse applications. The presentation of these models is “computational” in the sense that it is easily adapted to computer-based Monte Carlo simulation.

A guiding principle was to be as rigorous as possible without the use of measure theory. Some of the topics contained herein are:

• Fundamental limit theorems such as the weak and strong laws of large numbers, the central limit theorem, as well as the monotone, dominated, and bounded convergence theorems

• Markov chains with finitely many states

• Random walks on Z, Z2 and Z3

• Arrival processes and Poisson point processes

• Brownian motion, including basic properties of Brownian paths such as continuity but lack of differentiability

• An introductory look at stochastic calculus including a version of Ito’s formula with applications to finance, and a development of the Ornstein-Uhlenbeck process with an application to economics