Department of Mathematics and Statistics
Concordia University

Fall 2012

MAST 679N/MAST 881Z: Stochastic Differential Equations

R 10:30-13:00, LB-651 (SGW) note: change of time-room

Instructor: Lea Popovic
Office: LB 921-07 (SGW)
Phone: (514) 848-2424 Ext 5854

Office Hours: after class and by appointment

Course Outline

This course will provide an overview of stochastic differential equations useful for scientific modeling, guided by some problems in applications. It will cover basic theory including weak and strong approximation, efficient numerical methods and error estimates, the relation between stochastic differential equations and partial differential equations, and will additionally cover treatment of stochastic differential equations with jumps.
The main part of the course will cover:
  • Continuous time stochastic Processes:
        Examples, Filtrations, Stopping times, Brownian motion, Poisson process
  • Martingales:
        Optional sampling theorem and Doob's inequalities, Quadratic variation and covariaton, Martingale convergence theorem
  • Stochastic Integrals:
        Definition, Change of time variable, Change of Integrator, Ito's formula
  • Stochastic Differential Equations:
        Examples, Uniqueness of solutions of SDEs, Gronwall inequality for SDEs, Existence of solutions, Moment estimates
  • Diffusions:
        Generator for a diffusion process, Exit distributions in one dimension, Dirichlet problems, Harmonic functions, Parabolic equations
  • Properties of paths:
        Equations for probability distributions, Stationary distributions, Long term behaviour
  • Poisson random measure:
        Integration w.r.t. a Poisson random measure, Centered Poisson random measure, SDEs driven by Poisson measures


An advanced course in stochastic processes, including martingales, Brownian motion, and possibly familiarity with stochastic integration.


"An Introduction to Stochastic Differential Equations" by L. C. Evans (online).
"Lectures on Stochastic Analysis" by T. G. Kurtz (online).
"Basics of Stochastic Analysis" by T.Seppalainen(online).


Homework will be assigned approximately once every two weeks, during lecture. Students are encouraged to work together on homework problems, however each student must write up the homework set on their own. There will be a take-home test or project handed out in the last week of class and due a week later. The final grade will be evaluated using: Homework assignments 50%, Final exam 50%.

Important Dates

Lecture Schedule    Homework Schedule