Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
STT 881
Description:
Conditional expectation, martingales, stationary processes. Brownian motion, convergence in distribution, and the invariance principle.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Restrictions:
Open to doctoral students in the Statistics major or approval of department.
Description:
Random walks, transcience and recurrence. Martingales, martingale convergence theorem, Doob's inequality, optional stopping theorem. Stationary processes and Ergodic theorem. Brownian motion. Kolmogorov's continuity theorem, strong Markov property, the reflection principle, martingales related to Brownian motion. Weak convergence in C([0,1]) and D([0,1]), Donsker's invariance principle, empirical processes.