Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space

2012 ◽  
Vol 82 (8) ◽  
pp. 1549-1558 ◽  
Author(s):  
Brahim Boufoussi ◽  
Salah Hajji
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Functional Differential ◽  
Stochastic Functional

Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
Zhi Li ◽  
Jiaowan Luo
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Hurst Parameter ◽  
Stochastic Functional Differential Equations ◽  
Harnack Inequalities ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter

scholarly journals Almost Periodic Solutions to Impulsive Stochastic Delay Differential Equations Driven by Fractional Brownian Motion With 12 < H < 1

2021 ◽  
Vol 9 ◽  
Author(s):  
Lili Gao ◽  
Xichao Sun
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Delay Differential Equations ◽  
Functional Differential ◽  
Stochastic Functional

In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion. Moreover, the stability of the mild solution is obtained. To illustrate the results obtained in the paper, an impulsive stochastic functional differential equation driven by fractional Brownian motion is considered.

scholarly journals Smoothness and Gaussian Density Estimates for Stochastic Functional Differential Equations with Fractional Noise

2020 ◽  
Vol 8 (4) ◽  
pp. 822-833
Author(s):  
Nguyen Van Tan
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Malliavin Calculus ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Density Estimates ◽  
Fractional Noise ◽  
Gaussian Density ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we study the density of the solution to a class of stochastic functional differential equations driven by fractional Brownian motion. Based on the techniques of Malliavin calculus, we prove the smoothness and establish upper and lower Gaussian estimates for the density.

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