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Seminar: Leonid Mytnik

Department of Statistics Seminar Series
February 13, 2013
All Day
Cockins Hall (CH), Room 240

Title

Uniqueness and Non-uniqueness for Stochastic Heat Equations with Holder Continuous Coefficients

Speaker

Leonid Mytnik, Technion

Abstract

Note: This seminar is primarily hosted by the Mathematics Department.

We consider the question of uniqueness/non-uniqueness for stochastic partial differential equations (SPDEs). We focus on heat equations perturbed by a multiplicative noise, or the stochastic heat equations. Such equations with Hölder 1/2 coefficients arise in population models. Does pathwise uniqueness hold for such equations? In 1971, the analogous question for SDE’s was resolved in the affirmative by T. Yamada and S. Watanabe. As for stochastic heat equations we prove pathwise uniqueness in the case of Hölder coefficients of index γ > 3/4. We also prove that uniqueness in law, and hence pathwise uniqueness, fails in general for γ