Mathematics 548 - StochasticProcesses & Simulatn

The course will cover the following topics in the core of the theory of Random and Stochastic Processes.We will introduce the students to some fundamental stochastic processes such as discrete state Markov chains, Poisson processes, and Brownian motion, as well as an array of important stochastic models. Computer programming will be a central part of this course.The theoretical part of this course includes analysis of random walks, convergence of discrete and continuous-time Markov processes to stationarity, Poisson processes and other point processes, Brownian motion and a bit Martingale processes. In addition, we also offer a series of lectures on topics of stochastic simulations--introduction to Monte Carlo methods and computer modeling of stochastic systems. Monte Carlo topics that we will cover include random variable generation, expectation estimation with confidence interval formation, importance sampling, stochastic optimization, MCMC algorithms and sampling of Brownian motion.

CICS 110 and STATISTC 315