scholarly journals Transportation Inequalities for Coupled Fractional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Wentao Zhan ◽  
Yuanyuan Jing ◽  
Liping Xu ◽  
Zhi Li
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Hurst Parameter ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniform Distance

In this paper, we consider the existence and uniqueness of the mild solution for a class of coupled fractional stochastic evolution equations driven by the fractional Brownian motion with the Hurst parameter H∈1/4,1/2. Our approach is based on Perov’s fixed-point theorem. Furthermore, we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.

scholarly journals Existence and exponential stability of almost pseudo automorphic solution for neutral stochastic evolution equations driven by G-Brownian motion

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1075-1092
Author(s):  
Pengju Duan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Exponential Stability ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Evolution Operator ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

This paper mainly concerns the quasi sure exponential stability of square mean almost pseudo automorphic mild solution for a class of neutral stochastic evolution equations driven by G-Brownian motion. By means of evolution operator theorem and fixed point theorem, existence and uniqueness of square mean almost pseudo automorphic mild solution is obtained. Also, a series of sufficient conditions on exponential stability and quasi sure exponential stability are established.

scholarly journals Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Mild Solutions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Convergence Results ◽  
Real Separable Hilbert Space ◽  
Wave Phenomena

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.

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