Course 18.176, Fall 2013
This course is a rigorous introduction to stochastic analysis.
We will introduce stochastic processes, in particular the Brownian motion and the Poisson process. After reviewing some necessary elements
of martingale theory, we will define and study integration with respect to such processes. We will then show It\^o's formula.
This will bring us to stochastic partial differential equations. We will consider applications to partial differential equations, finance or statistical mechanics....
This course will require basic notions in probability theory,
18.175 should be more than enough. Grading will be based on homeworks.
Office hours: Tuesday 2:45PM-4:45PM
Course: Tuesday-Thursday 1-2:30 PM, E17-128
Lecture Notes
Problem set 1, due Tuesday, September 24
( Comments on Problem set 1 )
Problem set 2, due Thursday, October 10
Problem set 3, due Thursday, October 24
( Comments on Problem set 3 )
Problem set 4, due Thursday, November 7
Problem set 5, due Thursday, November 21
( Comments on Problem set 5 )
Problem set 6, due Thursday, December 5
Bibliography:
Daniel Revuz and Marc Yor; Continuous martingales and Brownian motion,
Jean-Francois Le Gall; Mouvement Brownien, martingales et calcul stochastique,
Ioannis Karatzas and Steven E. Shreve; Brownian motion and Stochastic calculus,
Bernt Oksendal; Stochastic Differential equations.