MATH5545 is a Mathematics Level V course. See the course overview below.

Units of credit: 6

Prerequisites: MATH3611 or equivalent

Cycle of offering: Session 1

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. (This pdf will usually be updated by the end of the first week of the session.)

The Online Handbook entry contains up-to-date timetabling information.

Stochastic Differential Equations (SDEs) have wide applications in Science, Engineering and Economics. It is worth to note that the concept of Brownian Motion (one of the building blocks in the theory of SDEs) was introduced by L. Bachelier in Economics and by A. Einstein in Statistical Physics almost at the same time at the beginning of the XX-th century. Another motivation for the theory of SDEs is their application to the analysis of deterministic partial differential equations. This application was the main motivation for K. Ito who developed a rigorous mathematical theory of SDEs in the early fifties of the XX-th century. Since that time SDEs were applied to study a large variety of linear and nonlinear partial differential equations like heat equation, Poisson equation, Hamilton-Jacobi equations and others.

In this course we will learn about basic properties of SDEs and their relationship with partial differential equations. Students are expected to have basic knowledge of Real Analysis and Measure Theory but only minimal background in Probability Theory is required. The course will be self-contained and no previous course on Stochastic Analysis is needed. Knowledge of Functional Analysis at a very elementary level would be welcome but not necessary.