15.070 Advanced Stochastic Processes

As taught in: Fall 2005

A stopped Brownian motion as an example for a martingale.

Some stopping times (even hitting times) of Brownian motion. (Image courtesy of Thomas Steiner.)

Level:

Graduate

Instructors:

Prof. David Gamarnik

Premal Shah

Course Features

Course Description

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.