$ p $th moment exponential stability and convergence analysis of semilinear stochastic evolution equations driven by Riemann-Liouville fractional Brownian motion

Abstract

<abstract><p>Many works have been done on Brownian motion or fractional Brownian motion, but few of them have considered the simpler type, Riemann-Liouville fractional Brownian motion. In this paper, we investigate the semilinear stochastic evolution equations driven by Riemann-Liouville fractional Brownian motion with Hurst parameter $ H < 1/2 $. First, we prove the $ p $th moment exponential stability of mild solution. Then, based on the maximal inequality from Lemma 10 in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, the uniform boundedness of $ p $th moment of both exact and numerical solutions are studied, and the strong convergence of the exponential Euler method is established as well as the convergence rate. Finally, two multi-dimensional examples are carried out to demonstrate the consistency with theoretical results.</p></abstract>