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We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…

Probability · Mathematics 2009-11-23 Stefano Bonaccorsi , Ciprian Tudor

We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stochastic Process. Appl., 2016). To this end, we extend the notion of non-linear Young equations to a…

Probability · Mathematics 2023-01-13 Florian Bechtold , Fabian A. Harang , Nimit Rana

We consider the stochastic continuity equation perturbed by a fractional Brownian motion and the drift is allowed to be discontinuous. We show that for almost all paths of the fractional Brownian motion there exists a solution to the…

Probability · Mathematics 2018-06-26 Torstein Nilssen

In this paper, we study a class of dissipative stochastic differential equations driven by nonlinear multiplicative fractional Brownian noise with Hurst index $H \in \left(\frac{1}{3},\frac{1}{2})\cup(\frac{1}{2}, 1\right) $. We establish…

Probability · Mathematics 2025-10-02 Qiyong Cao , Hongjun Gao , Wei Wei

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 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

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in…

Probability · Mathematics 2012-03-14 Marco Ferrante , Carles Rovira

In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such equation. We now consider the case of…

Probability · Mathematics 2013-11-20 Serge Cohen , Fabien Panloup , Samy Tindel

We present an innovating sensitivity analysis for stochastic differential equations: We study the sensitivity, when the Hurst parameter~$H$ of the driving fractional Brownian motion tends to the pure Brownian value, of probability…

Probability · Mathematics 2017-02-14 Alexandre Richard , Denis Talay

We consider the rough differential equations driven by tempered fractional Brownian motion with Hurst index $H\in (\frac{1}{4}, \frac{1}{3})$ and tempered parameter $\lambda>0$. First, by means of piecewise linear approximation, we…

Dynamical Systems · Mathematics 2026-03-10 Lijuan Zhang , Jianhua Huang

The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems…

Analysis of PDEs · Mathematics 2013-07-19 Elena Issoglio

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

We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with…

Probability · Mathematics 2013-07-25 Martin Hairer , Natesh S. Pillai

We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hurst parameter $H>\frac{1}{3}$. The system is analyzed using…

Probability · Mathematics 2026-02-10 Eliseo Luongo , Francesco Triggiano

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…

Numerical Analysis · Mathematics 2022-01-27 Daxin Nie , Jing Sun , Weihua Deng

In this work we study the smoothing effect of rough differential equations driven by a fractional Brownian motion with parameter $H>1/4$. The regularization estimates we obtain generalize to the fractional Brownian motion previous results…

Probability · Mathematics 2013-04-18 Fabrice Baudoin , Cheng Ouyang , Xuejing Zhang

The well-posedness is investigated for distribution dependent stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (\ff {\sq 5-1} 2,1)$ and distribution dependent multiplicative noise. To this…

Probability · Mathematics 2024-11-13 Xiliang Fan , Shao-Qin Zhang

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

We show that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative…

Analysis of PDEs · Mathematics 2020-08-04 Zdzisław Brzeźniak , Jakub Slavík

This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…

Probability · Mathematics 2025-01-28 Jiaohui Xu , Tomás Caraballo , José Valero