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In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…

Probability · Mathematics 2013-11-05 Aurélien Deya , Samy Tindel

This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a…

Dynamical Systems · Mathematics 2013-05-30 Y. Chen , H. Gao , M. J. Garrido-Atienza , B. Schmalfuss

In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2019-04-23 Jian Song , Xiaoming Song , Fangjun Xu

We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…

Probability · Mathematics 2025-07-01 Maximilian Buthenhoff , Ercan Sönmez

In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H…

Probability · Mathematics 2023-02-09 Mireia Besalú , David Márquez-Carreras , Carles Rovira

The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$. We would like to emphasize that we do not use the usual cohomology…

Analysis of PDEs · Mathematics 2013-07-26 H. Gao , M. J. Garrido-Atienza , B. Schmalfuss

Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u}d\mu(u), \;\; 0\leq t\leq 1{equation} A different…

Probability · Mathematics 2011-07-20 Mamadou Abdoul Diop , Youssef Ouknine

A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…

Mathematical Physics · Physics 2011-07-15 Jin Li , Jianhua Huang

In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that…

Probability · Mathematics 2007-05-23 Fabrice Baudoin , Laure Coutin

This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…

Analysis of PDEs · Mathematics 2016-09-09 Hakima Bessaih , María J. Garrido-Atienza , Xiaoying Han , Björn Schmalfuß

In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic…

Probability · Mathematics 2026-04-03 Johanna Garzón , Jorge A. León , Jorge Lozada , Soledad Torres

The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with $H>\tfrac{1}{2}$. For this, we summarise the theory of fractional white noise and prove a fundamental $L^2$-estimate for…

Probability · Mathematics 2026-05-25 Jasmina Đorđević , Bernt Øksendal

This paper deals with the well posedness of an integrodifferential equation that describes a vortex filament associated to a 3D turbulent fluid flow. This equation is driven by a fractional Brownian motion of Hurst parameter H>1/2. We prove…

Probability · Mathematics 2011-03-18 Hakima Bessaih , Chandana Wijeratne

In this article, we study differential equations driven by continuous paths with with bounded $p$-variation for $1 \leq p< 2$ (Young systems). The most important class of examples of theses equations is given by stochastic differential…

Analysis of PDEs · Mathematics 2014-12-08 R. A. Castrequini , P. J. Catuogno

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations…

Analysis of PDEs · Mathematics 2017-05-05 Luu Hoang Duc , María J. Garrido-Atienza , Andreas Neuenkirch , Björn Schmalfuß

The paper suggests a way of stochastic integration of random integrands with respect to fractional Brownian motion with the Hurst parameter H> 1/2. The integral is defined initially on the processes that are "piecewise" predictable on a…

Probability · Mathematics 2020-04-21 Nikolai Dokuchaev

In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the…

Probability · Mathematics 2016-02-24 Shuwen Lou , Cheng Ouyang

This paper studies a stochastic functional differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2, constrained to be reflected at 0. We prove the existence of solutions using the Euler method. However,…

Probability · Mathematics 2024-10-02 Chadad Monir

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for $H>1/2$ define flows of homeomorphisms on $\mathbb{R}^{d}$.

Probability · Mathematics 2007-05-23 L. Decreusefond , D. Nualart

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske