p " role="presentation"> p p p th moment exponential stability and convergence analysis of semilinear stochastic evolution equations driven by Riemann-Liouville fractional Brownian motion

AIMS Mathematics

article

Xueqi Wen¹  Zhi Li¹ 

[1] School of Information and Mathematics, Yangtze University

关键词: semilinear stochastic evolution equation;    Riemann-Liouville fractional Brownian motion;    $ p $th moment exponential stability;    exponential Euler method;    strong convergence;   

DOI  :  10.3934/math.2022806

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY