Weyl Pseudo Almost Periodic Type Solutions to Semilinear Stochastic Evolution Equations Driven by Fractional Brownian Motion

Abstract

In this paper, we analyze square-mean Weyl almost periodic solutions and square-mean Weyl double-measure pseudo almost periodic solutions for a class of semilinear evolution equations in separable Hilbert spaces driven by two-sided fractional Brownian motion with Hurst index $H<1/2$. Due to the non-integrability of covariance density for $H<1/2$, a Hölder-continuity condition on the diffusion coefficient is required. An illustrative example involving a stochastic parabolic equation demonstrates the applicability of obtained results.