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.

  • Local Times