Course Description
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.
Spring 2026
Instructors
Meeting Patterns
Classes Start:
January 12, 2026
Classes End:
April 28, 2026
Location:
02112 Williams Hall
Class Days:
T H
Class Start Time:
11:45am
Class End Time:
1:00pm
Class Type:
Lecture
Credits:
3.00
Restrictions:
Prerequisite: MA(ST) 546