MATH 471 - Markov Models

3 units (fi 6)(EITHER, 3-0-0)

Birth-death processes; continuous-time Markov chains; functional central limit theorem; Brownian motion; weak solutions to stochastic differential equations; weak uniqueness; filtrations; discrete and continuous martingales; martingales problems; strong Markov property; Kolmogorov forward and backward equations; stationary distributions; null and positive recurrence; transience; particle filtering. Prerequisite: STAT 281 or STAT 371. Note: Credit cannot be obtained in MATH 471 if credit has already been in STAT 471.

STAT 471 - Probability I

3 units (fi 6)(EITHER, 3-0-0)

Probability spaces, algebra of events. Elements of combinatorial analysis. Conditional probability, stochastic independence. Special discrete and continuous distributions. Random variables, moments, transformations. Basic limit theorems. Prerequisite: One of STAT 371 or STAT 281.