Anja Sturm
University of Delaware
Title: Strong uniqueness for the stochastic heat equation with singular colored noise.

Motivated by the still open question of strong uniqueness for the stochastic heat equation with white noise associated with super-Brownian motion we investigate this problem in a colored noise setting. We generalize arguments by Yamada and Watanabe in order to show strong uniqueness for the heat equation with a multiplicative colored noise term for any dimension. Here, the noise coefficient is Hölder continuous in the solution and the noise is white in time but spatially correlated (translation invariant) with the correlation function either bounded or singular at the origin. Our condition for uniqueness relates the Hölder exponent of the noise coefficient with the singularity of the noise.

This is joint work with Ed Perkins and Leonid Mytnik.
©2004, Department of Mathematical Sciences
Last Modified: September 23, 2004