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.