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Advanced development of stochastic processes. Conditional expectation, filtrations of sigma-algebras, stopping times. Martingales, associated convergence theorems and inequalities, martingale decomposition, optional stopping. Markov chains including random walks, recurrence versus transience, asymptotic behavior. General Markov processes and the related semigroup operators. Construction and properties of Brownian motion, Donsker's invariance principle. Other potential topics include stationary processes, Birkhoff's ergodic theorem, branching processes, Poisson processes.

Prerequisite: MA(ST) 546

Typically offered in Spring only