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.
Stochastic Processes, Ross, Wiley, 2nd edition.
MATH 765 or permission of the instructor.
A stochastic process is a collection of random variables depending on a discrete or continuous time parameter. Stochastic or random processes are mathematical models for empirical date in a variety of areas as medicine, biology, physics, engineering, economics and psychology. The aim of this course is to study some basic examples of stochastic processes.
- Markov chains.
- Martingales with discrete time.
- Poisson processes.
- Continuous-time Markov chains.
- Renewal theory.
- Brownian motion.
(Pasik-Duncan 2009 )