Introduction to Stochastic Processes

This concise, informal introduction to stochastic processes evolving with time was designed to meet the needs of graduate students not only in mathematics and statistics, but in the many fields in which the concepts presented are important, including computer science, economics, business, biological science, psychology, and engineering.

With emphasis on fundamental mathematical ideas rather than proofs or detailed applications, the treatment introduces the following topics:

Markov chains, with focus on the relationship between the convergence to equilibrium and the size of the eigenvalues of the stochastic matrix

Infinite state space, including the ideas of transience, null recurrence and positive recurrence

The three main types of continual time Markov chains and optimal stopping of Markov chains

Martingales, including conditional expectation, the optional sampling theorem, and the martingale convergence theorem

Renewal process and reversible Markov chains

Brownian motion, both multidimensional and one-dimensional

Introduction to Stochastic Processes is ideal for a first course in stochastic processes without measure theory, requiring only a calculus-based undergraduate probability course and a course in linear algebra.