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This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2019-07-02 Xi Geng , Cheng Ouyang , Samy Tindel

In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a…

Probability · Mathematics 2022-07-05 Xiliang Fan , Ting Yu , Chenggui Yuan

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2020-08-05 Xi Geng , Cheng Ouyang , Samy Tindel

This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density…

Probability · Mathematics 2014-01-16 Fabrice Baudoin , Eulalia Nualart , Cheng Ouyang , Samy Tindel

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 a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

Probability · Mathematics 2011-11-09 Yuliya Mishura , Georgiy Shevchenko

This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter $H\in(\frac{1}{2},1)$. We firstly prove that the equation has a unique…

Probability · Mathematics 2023-12-12 Wei Wei , Hongjun Gao , Qiyong Cao

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise,…

Probability · Mathematics 2016-08-11 M. Besalú , A. Kohatsu-Higa , S. Tindel

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 shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…

Probability · Mathematics 2015-11-03 José Luís da Silva , Mohamed Erraoui , El Hassan Essaky

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

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…

Probability · Mathematics 2019-04-08 H. Araya , J. A. León , S. Torres

We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional…

Probability · Mathematics 2010-05-27 Igor Cialenco

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

This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…

Probability · Mathematics 2021-09-29 Adnan Aboulalaa

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed…

Probability · Mathematics 2012-06-28 K. Kubilius , Y. Mishura

We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…

Statistics Theory · Mathematics 2025-12-23 Chiara Amorino , Eulalia Nualart , Fabien Panloup , Julian Sieber

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

Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…

Probability · Mathematics 2017-01-06 Oussama El Barrimi , Youssef Ouknine

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2012-03-05 Mireia Besalú , Carles Rovira