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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