15.070 Advanced Stochastic Processes

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.)

Course Highlights

This course features a complete set of lecture notes from the instructor, together with the assignments and exams.

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.
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Staff

Instructors:
Prof. David Gamarnik
Premal Shah

Course Meeting Times

Lectures:
Two sessions / week
1.5 hours / session

Recitations:
One session / week
1 hour / session

Level

Graduate