IEMS 460-2 Stochastic Models 2

Spring 2012

Last modified: Tue Jun 12 21:56:10 CDT 2012

Lectures: Monday Wednesday Friday 10:00-10:50 in Tech LG72

Instructor: Benjamin Armbruster
Office Hours Wednesdays 4-5 in Tech M237


Topics Covered

Modes of convergence for random variables
Big-O, little-o notation

Renewal processes (RPs)
Renewal theorems
Alternative renewal processes (ARPs)
Regenerative processes
Renewal-reward process
Semi-Markov processes (SMPs)
Phase-type distributions

Random walks
Duality and Wiener-Hopf Factorization
M/M/1, G/M/1 queues

Discrete time martingales
Exponential martingales
Optional stopping

Brownian motion
Donsker's theorem
Stochastic differential equations (SDEs) and partial differential equations (PDEs)

Sequential Hypothesis Testing
Markov Chain Monte Carlo
Gibbs sampler
Gaussian processes
Probability inequalities


The following Wikipedia pages were created or improved as part of students' course projects: Stochastic Programming, Optimal Stopping, Quasi-Monte Carlo, Branching Process, Jackson Network, Uncertainty Quantification, Karhunen-Loeve Theorem