The class on Oct 23 will start from 14:30.

1. Introduction & Purposes

In this short course on diffusion processes, we will first go over basic facts on Brownian

motion, stochastic integral and Ito’s formula, and then introduce diffusion processes as

solutions to stochastic differential equations driven by Brownian motion. The last part

of this course is an introduction of recent work on threshold diffusions, which solve the

stochastic differential equations with step-function drift and diffusion coefficients.

2. Outline & Descriptions

Lecture 1: Brownian motion as a Gaussian process, as a Markov process and as a martingale,

the zero set of Brownian motion;

Lecture 2: stochastic integral, Ito’s formula and stochastic differential equations;

Lecture 3: basics of diffusion processes, threshold diffusion and its exit problem, potential

measure and transition density

3. References

1. Richard Durrett (1996): Stochastic Calculus: A Practical Introduction. CRC Press.

2. Gregory F. Lawler (2006): Introduction to Stochastic Processes. Chapman & Hall/CRC.

4. Registration

https://forms.gle/Y5XWvykv8g5WM66u8