Stochastic fractional diffusion equations with spatial Gaussian noise in the Stratonovich regime

Abstract

For a class of stochastic fractional diffusion equations, we prove the existence of Stratonovich solutions and obtain the precise values of the Lyapunov exponents governing the large $t$-asymptotics of their $p$-th moments for all real $p\in \{1\}\cup [2,\infty )$, as well as the large $p$-asymptotics of the $p$-th moments.