"Local time of discrete stochastic processes and a homogenization problem”

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Speaker: Xiaofei Zheng, Adviser: Manfred Denker, Penn State

Abstract: Suppose {X_i} are i.i.d or strictly stationary, S_n is the partial sum of {X_i}. We are interested in studying the time that S_n spends at a certain level and its limiting behavior. For continuous stochastic processes, it is described by local time. Levy first introduced Brownian local time in 1939. For discrete processes, we are looking for a good definition of local time. We defined the local time of a random walk, it turns out that after a proper scaling, the local time converges to the Brownian local time. For discrete martingale, I will introduce how to embed it into the path of a Brownian motion, and study the downcrossing number. In the second part of my talk, I will introduce the problem of homogenization driven by fractional Brownian motion. Based on the work of Iyer, Komorowski, Novikov and Ryzhik, we conjecture that the solution to dX_t=-AV(X_t)dt+dB^H(t) converges to Brownian motion weakly. The possible method is to introduce stopping times and study the number of downcrossings.

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Room Reservation Information

Room Number: 114 McAllister

Date: 10/07/2014

Time: 3:40pm - 5:40pm