Math 865, Spring 2004

Introduction to Stochastic Processes

Markov chains; Markov processes; diffusion processes; stationary processes. Emphasis is placed on applications; random walks; branching theory; Brownian motion; Poisson process; birth and death processes.
Text: Introduction to Probability Models, Ross, Academic Press, 7th edition.

Prerequisite: Math 627 and MATH 765 or permission of the instructor.

Credit Hours: 3

The theory of stochastic processes is generally defined as the "dynamic" part of probability theory, in which one studies a collection of random variables (called stochastic process) from the point of view of their interdependence and limiting behavior. One is observing a stochastic process whenever one examines a process developing in time in a manner controlled by probabilistic laws. Stochastic or random processes occur in medicine, biology, physics, engineering, oceanography, economics, and psychology, to name only a few scientific disciplines.

This course has three aims:

• to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models;
• to provide an introduction to the methods of probability model-building;
• to provide the student who does not possess an advanced mathematical background with mathematically sound techniques to enable further study of the theory of stochastic processes.

The Wiener process, Poisson process, renewal counting processes, queues, Markov chains (discrete and continuous), random walks, and birth and death processes will be introduced and discussed. New applications will be presented

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