Brownian motion and stochastic analysis

This is a six-week graduate-level course designed for students with a major in mathematics, applied mathematics, physics, or computer science. The course introduces the student to the key techniques to work with Brownian motion, stochastic integration, martingales, and Ito’s formula. The course content includes topics such as Brownian motion, stochastic integral, Ito’s formula and applications.

Study material:

• Le Gall, J.-F. Brownian Motion, Martingales, and Stochastic Calculus. Graduate Texts in Mathematics, 2016
• Durrett, R. Stochastic calculus: a practical introduction. CRC Press, Probability and Stochastics Series, 1996
• Berestycki, N. Stochastic calculus. Online lecture notes