Statistics and Probability Seminar

Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition
Friday, 3 March 2017 - 1:30 pm to 2:00 pm
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SPEAKER: Raluca Balan (uOttawa) DATE: Friday, March 3, 2017 TIME: 1:30 pm ROOM: KED B015 ABSTRACT: The goal of this talk is to illustrate how various quantitative properties of the noise combined with the roughness of the initial condition may affect the existence of a random field solution of an SPDE, and to describe the impact of the noise and the initial condition on the behaviour of this solution. More precisely, we will consider the Parabolic Anderson Model driven by a space-time homogeneous Gaussian noise, with initial condition given by a signed measure. We assume that the covariance kernels of the noise in space and time are given by locally integrable non-negative-definite functions. We show that the solution to this equation exists and has a Holder continuous modification, under the same respective conditions as in the case of the white noise in time. This shows that the temporal structure of the noise has no effect on the existence and Holder regularity of the solution. However, the smoothness of the noise in time plays a big role in the order of magnitude of the moments of the solution. This talk is based on joint work with Le Chen (University of Kansas).