Stochastic Analysis II/Stochastic Differential equations

Jan 5, 2027 — Apr 27, 2027

About the course

This is a one semester three credit hour course. It is about the theory and applications of stochastic differential equations driven by Brownian motions.

The stochastic differential equations have found applications in finance, signal processing, population dynamics, biology, and many other fields. It is the basis of some other applied probability areas such as filtering theory, stochastic control and stochastic differential games.

To balance the theoretical and applied aspects and to include as much audience as possible, we shall focus on the stochastic differential equations driven only by Brownian motion (white noise). We will focus on the theory and not get into specic applied area (finance, signal processing, filtering, control and so on).

We shall first briefly introduce some basic concepts and results on stochastic processes, in particular the Brownian motions. Then we will discuss stochastic integrals, Ito formula, the existence and uniqueness of stochastic differential equations, some fundamental properties of the solution. We will concern with the Markov property, Kolmogorov backward and forward equations, Feynman-Kac formula, Girsanov formula. We will also concern with the ergodic theory and other stability problems. We may also mention some results on numerical simulations, Malliavin calculus and so on.

Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

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