Probability Theory II, MATH 711/STAT 811

Instructor: George Androulakis, my web site, my email: giorgis@math.sc.edu and my office phone number: (803)777-7539.
Lectures: MWF 12-12:50 in LeConte 315.
Office Hours: MWF 9:45-10:45 or by appointment in my office (LeConte 402).

The theory of probability is very useful in Mathematics! It plays an important role in both pure and applied mathematics. More precisely, Probability theory is useful in Combinatorics, Stochastic Analysis, Functional Analysis, Mathematical Modeling, Theory of Machine Learning, Classical and Quantum Information Theory. Outside of Mathematics, Probability theory is important in Statistics, Physics (such as in Statistical Physics), Data Science, Computer Science (for example in probabilistic algorithms), Game Theory, and Economics/Finance.

Textbook: Achim Klenke, Probability Theory, A comprehensive course, Third Edition. Springer, Universitext, 2020.

Instructional Objectives:
We will choose from the following topics:

• Basic Measure Theory.

• Independence.

• Laws of Large Numbers.

• Conditional Expectations.

• Martingales.

• Convergence of measures.

• Central Limit Theorem.

• Markov Chains.

• Brownian Motion.

• Itô Integral.

Prerequisites: The class will be appropriate for all graduate students.

Grading: The grade will be based on homework.