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

Abstract

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 pth moment exponential stability of mild solution. Then, based on the maximal inequality from Lemma 10 in [1], the uniform boundedness of pth 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.

Keywords

• semilinear stochastic evolution equation
• riemann-liouville fractional brownian motion
• pth moment exponential stability
• exponential euler method
• strong convergence