### Analysis Learning SeminarBrownian Motion and Ito's IntegralMarco Carfagnini (UConn)

Friday, September 20, 2019
3:30pm – 4:30pm

Storrs Campus
Monteith 214

This talk is a short review of basic stochastic calculus. We will define a stochastic process first, and then focus on the (real-valued) Brownian motion and its properties (independence of the increments, regularity of paths etc). Afterwards, we will define the Ito's integral and state Ito's Lemma. In particular, we will see why analytic construction (such as Riemann-Stieltjes integral) can not be applied to define the integral of a function against the Brownian motion. No graduate probability course is needed as prerequisite.

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