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Probability and Computational Finance Seminar
Fraydoun Rezakhanlou
UC Berkeley
Title: Diffusions with Rough Drifts

Abstract: According to DiPerna-Lions theory, velocity fields with weak derivatives in $L^p$ spaces possess weakly regular flows. When a velocity field is perturbed by a white noise, the corresponding (stochastic) flow is far more regular in spatial variables; a diffusion with a drift in a suitable $L^p$ space possesses weak derivatives with exponential bounds.

As an application we show that a Hamiltonian system that is perturbed by a white noise produces a symplectic flow for a Hamiltonian function that is merely in $W^{1,p}$ for $p$ strictly larger than dimension. I also discuss the potential application of such regularity bounds to study solutions of Navier-Stokes equation with the aid of Constantin-Iyer's circulation formula.

Date: Monday, April 14, 2014
Time: 5:00 pm
Location: Wean Hall 8427
Submitted by:  Gautam Iyer
Note: Please note the change of room