KIT - Department of Mathematics - Pathwise uniqueness for stochastic differential equations on Hilbert spaces

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PDE-Seminar: Talk by Michael Röckner

PDE-Seminar: Talk by Michael Röckner

Pathwise uniqueness for stochastic differential equations on Hilbert spaces

Speaker: Prof. Dr. Michael Röckner
Place: Seminar room 1.067, Building 20.30
Time: 26.1.2017, 14:00 - 15:00
Invited by: CRC 1173

Abstract

In a seminal paper from 1978 A. Veretennikov proved that for strictly elliptic and Lipschitz multiplicative noise, merely measurability and boundedness of the coefficients already imply pathwise uniqueness for solutions of a stochastic differential equation (SDE) on $\mathbb{R}^d$ . This result is heavily based on elliptic regularity results for the corresponding Kolmogorov operator. In this talk we shall present a corresponding result in infinite dimensions, more precisely a pathwise uniqueness result for SDEs on Hilbert spaces. We shall first explain this "regularization by noise" phenomenon in terms of the corresponding linear Fokker-Planck-Kolmogorov equation. Some very recent developments on the subject will be presented at the end of the talk.