Continuity with respect to the Hurst parameter of solutions to stochastic evolution equations driven by H-valued fractional Brownian motion

Abstract

In this work, the continuity with respect to the Hurst parameter of solutions to stochastic evolution equations is studied. Compared with recent studies on such continuity property, the model here is considered in a different point of view in which the equations are of SPDEs type, the solution and the fractional Brownian motion take value on a Hilbert space. The main contribution is to investigate the existence and stability of the solution with respect to the Hurst index in the space .