|Random walks, Brownian motion and Donsker’s invariance principle|
|Time：||Tue/Thu 15:10-17:00, 2015-07-21 ~ 2015-08-13|
|Instructor：||Xinxin Chen [University Lyon 1]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building|
The random walk with i.i.d. steps, as a discrete analog of Brownian motions (or stable processes), serves as a fundamental tool in the research of many random models. As stated in Donsker’ theorem, its rescaling trajectory converges to Brownian motion.
This mini course will prove Donsker’s invariance principle by two different ways. The first is classical and the second based on Skorokhod’s embedding theorem. We’ll see some applications of Donsker’s invariance principle and its extensions, like convergence towards Brownian bridge/excursion.
Basic understanding of probability theory, including one-dimensional Brownian motion, weak convergence.
Billingsley, P. (1999) Convergence of Probability Measures.\