Applied Stochastic Processes { Math 564 Fall 2011 Syllabus
Lee DeVille · 2011
nal. The homeworks will be worth 50% of the nal grade and the exams each 25%. Homework will be collected each Monday in class. Course material: The bulk of the material will be using Norris’ book. We will follow the book sequentially and occasionally we will supplement with material from other sources. Main topics: Discrete-time MC: classes, hitting times, absorption probabilities, recurrence and transience, invariant distributions and convergence to same, reversibility, ergodic theorems Continuous-time MC: same topics as above, holding times, explosion, forward/backward Kolmogorov equations Related topics: Martingales, potential theory, Brownian motion, ltering and estimation Applications: Queuing theory, population biology, Markov chain Monte Carlo methods Prerequisites: Students in this class should have some background in probability theory, linear algebra, and analysis. We will develop the necessary measure theory in the course as needed.