Spring 2018 
01/22  Huy Ba Dinh  Why we want stochastic integration (ideas from time series such as autoregressive models, scaling limits of difference equations with noise), brief review of LebesgueStieltjes integration (especially integration with respect to functions of bounded variation), proof that Brownian motion is not of bounded variation, proof that it is nowhere differentiable 
01/29  Rebekah Eichberg  Brief review of discrete time martingales (especially Doob's decomposition for submartingales), continuous time martingales, quadratic variation process of a local martingale, local martingales versus martingales (give an example) 
02/05  Yiming Xu  Construction of stochastic integrals for Brownian motion

02/12  Curtis Miller  Ito's formula and applications/examples, Levy characterization of Brownian motion, continuous martingales as time changed Brownian motions 
02/26  Curtis Miller  Ito's formula and applications/examples, Levy characterization of Brownian motion, continuous martingales as time changed Brownian motions 
03/05  Yiming Xu  Some special SDEs: OrnsteinUhlenbeck processes, geometric Brownian motion, Bessel processes. The notion of local time. 
03/12  Weicong Su  Stochastic differential equations: existence and uniqueness for the Lipschitz case

03/26  Sergazy Nurbavliyev  Girsanov formula, special properties of 2dimensional Brownian motion 
03/26  person a  topic 8 
04/02  person b  topic 9 
04/09  person c  topic 10 
04/16  person d  topic 11 
04/23  person e  topic 12 