Semester:
Fall of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828 or concurrently
Description:
Measures and their extensions, integration, and convergence theorems. Product measures, Lebesgue decomposition, transition probabilities, Kolmogorov consistency theorem. Independence. Classical limit theorems for partial sums.
Semester:
Fall of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Prerequisite:
STT 861 and MTH 421
Restrictions:
Open to doctoral students in the Statistics major or approval of department.
Description:
Measures and their extensions, integration. Lp spaces and Inequalities. Lebesgue decomposition, the Radon-Nikodym theorem. Product measures, Fubini's theorem. Kolmogorov consistency theorem. Independence, Kolmogorov's zero-one law, the Borel-Cantelli lemma. Law of large numbers. Central limit theorems, characteristic functions, the Lindeberg-Feller theorem, asymptotic normality of sample median. Poisson convergence. Conditional expectations.