Advanced Stochastic Processes

MATH8007, Fall semester, 2020

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall

Teaching mode

• All the lectures will be online, mixed with asynchronous and synchronous ones. Lecture times Fri 4:30-5:45pm.
• All lectures (videos) will be available via Canvas.
• Individual online meetings, in place of traditional OH, by email appointment (preferably Thurs b/w 4:30 and 6pm).

Course description

The course will cover a series of classical stochastic models, and emphasize on the analysis of their asymptotic behaviors (limit theorems).

Lecture notes are available on Canvas. There will be minor updates as semester goes (do not print them all at once).

Pre-req: Applied probability (MATH 6008) or equivalent would be helpful.

Grades

There will be 5-7 homework/project sets. No exams.

Tentative Schedule

• Week 1 (Aug 24): Review of first course in measure-theoretic probability.
• Week 2 (Aug 31): Stable distributions and a central limit theorem.
• Week 3 (Sep 7): Labor Day, Sep 7, Mon. Stochastic processes, an overview.
• Week 4 (Sep 14): Brownian motion.
• Week 5 (Sep 21): Modulus of continuity of Brownian motion.
• Week 6 (Sep 28): Donsker's theorem.
• Week 7 (Oct 5): Limit theorems for linear processes.
• Week 8 (Oct 12): Conditional expectations.
• Week 9 (Oct 19): Martingales.
• Week 10 (Oct 26): Brownian motion as a martingale
• Week 11 (Nov 2): Polya's urn model.
• Week 12 (Nov 9): Veterans Day Holiday, Nov 11, Wed. Chinese restaurant processes.
• Week 13 (Nov 16):
• Week 14 (Nov 23):
• Week 15 (Nov 30): Class ends Dec 2, Wed

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