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

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 ^[1], 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.