Probability and Stochastic Processes II

3 Credits.

The Probability and Stochastic Processes I and II course sequence allows the student to more deeply explore and understand probability and stochastic processes. The second course in the sequence is an introduction to theory and applications of stochastic processes. We start with a brief review of material covered in EN.625.721 . We move onto Gaussian random vectors and processes, renewal processes, renewal reward process, discrete-time Markov chains, classification of states, birth-death process, reversible Markov chains, branching process, continuous-time Markov chains, limiting probabilities, Kolmogorov differential equations, approximation methods for transition probabilities, random walks, and martingales. This course is proof oriented.