Existence and uniqueness of mild solution to fractional stochastic heat equation

Kostiantyn Ralchenko, Georgiy Shevchenko

Published 2018-11-29Version 1

For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and driven by an $L^2(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, we establish a new result on existence and uniqueness of a mild solution. Compared to the existing results, we show uniqueness in a fully nonlinear case, not assuming the coefficient in front of the noise to be affine. Additionally, we establish existence of moments for the solution.