| 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 Lebesgue-Stieltjes 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
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| 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: Ornstein-Uhlenbeck 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
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| 03/26 | Sergazy Nurbavliyev | Girsanov formula, special properties of 2-dimensional 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 |
