The class meets Mondays 5.10-7.00 PM in room 101 ground floor of Warren Weaver Hall.
Prerequsite: G63.2901 Basic Probability or equivalent.

Outline:

Review of basic probability and useful tools. Bernoulli trials and random walk. Law of large numbers and central limit theorem. Conditional expectation and martingales. Brownian motion and its simplest properties. Diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus. Feynman-Kac and Cameron-Martin Formulas. Applications as time permits.

Information

Answers

Measure theory

Independent Random variables

Martingales I

Martingales II

Assignment 1

Markov Chains

Assignment 2

Brownian Motion

Assignment 3

Brownian Motion II

Assignment 4

Stochastic Integrals

Assignment 5

Stochastic Differential equations

Assignment 6

Diffusion Processes

Assignment 7

Connection with PDE

Dynamic Programming

Markov Chain Approximations.

Assignment 8
Assignment 9

Take Home Final

Brownian Motion on a half space.

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