scholarly journals The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion

2011 ◽  
Vol 74 (11) ◽  
pp. 3671-3684 ◽  
Author(s):  
T. Caraballo ◽  
M.J. Garrido-Atienza ◽  
T. Taniguchi
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Evolution Equations ◽  
Exponential Behavior ◽  
Stochastic Delay

scholarly journals Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Peiguang Wang ◽  
Yan Xu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Delay Differential Equations ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Delay Differential

In this paper, we investigate the stochastic averaging method for neutral stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H∈1/2,1. By using the linear operator theory and the pathwise approach, we show that the solutions of neutral stochastic delay differential equations converge to the solutions of the corresponding averaged stochastic delay differential equations. At last, an example is provided to illustrate the applications of the proposed results.

Error estimates of a finite element method for stochastic time-fractional evolution equations with fractional Brownian motion

2021 ◽  
pp. 2250006
Author(s):  
Jingyun Lv
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Error Estimates ◽  
Evolution Equations ◽  
Fractional Evolution Equations ◽  
Backward Euler ◽  
Stochastic Time ◽  
Element Method

The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion. The spatial and temporal regularity of the mild solution is given. The numerical scheme approximates the problem in space by the Galerkin finite element method and in time by the backward Euler convolution quadrature formula, and the noise by the [Formula: see text]-projection. The strong convergence error estimates for both semi-discrete and fully discrete schemes are established. A numerical example is presented to verify our theoretical analysis.

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