STAT 410/MATH 310 - Random Processes and Applications
STAT 410/MATH 310 covers the following topics: Theory and applications of stochastic processes. Properties and applications of specific probability distributions. Properties of conditional distributions, and conditional expectations. Distributions of sums of independent random variables. Properties of random sums. Properties of multivariate normal distributions. Introduction to random walks, Markov chains, Poisson processes, birth and death processes, Brownian motion, Gaussian processes, and martingales.
Prerequisites: MATH 231 or Math 309. More generally a semester of probability theory. Multiple integrals and elementary matrix theory are used in the course.
Why is it interesting for Probabilistic Modelers?
Probability modeling and its applications requires probabilistic intuition as well as mathematical
theory and technique. Various examples of conditioning arguments strengthen the students’
understanding of this subtle concept. The theory keeps all the result on a firm foundation. The
technique allows one to compute solutions to complex problems.
The concepts and processes studied form building blocks that probabilistic modelers can use to build more complex models for specific real world situations. Examples of questions asked and problems that can be solved in terms of these fundamental models can guide the probabilistic modeler in new situations.
Offered every fall semester and spring semester.