On a class of stochastic fractional heat equations

Jian Song, Meng Wang, Wangjun Yuan

Published 2023-11-21Version 1

Considering the stochastic fractional heat equation driven by Gaussian noise with the covariance function defined by the heat kernel, we establish Feynman-Kac formulae for both Stratonovich and Skorohod solutions, along with their respective moments. One motivation lies in the occurrence of this equation in the study of a random walk in random environment which is generated by a field of independent random walks starting from a Poisson field.