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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

We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a…

Probability · Mathematics 2019-08-16 Fabian A. Harang , Marc Lagunas-Merino , Salvador Ortiz-Latorre

The Malliavin differentiability of a SDE plays a crucial role in the study of density smoothness and ergodicity among others. For Gaussian driven SDEs the differentiability property is now well established. In this paper, we consider the…

Probability · Mathematics 2023-05-18 Jorge A. León , Yanghui Liu , Samy Tindel

In this article we study a class of singular stochastic differential equations driven by fractional Brownian motion with Hurst parameter H<1/2. The solution is constructed as the limit of a family of approximating processes, and its…

Probability · Mathematics 2026-04-14 Xiaoming Song , Alexander Tortoriello

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…

Probability · Mathematics 2018-05-23 Soukaina Douissi , Jiaqiang Wen , Yufeng Shi

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

In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition…

Probability · Mathematics 2007-06-13 Jorge A. Leon , Jaime San Martin

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 discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic…

Probability · Mathematics 2024-05-10 Minoo Kamrani , Kristian Debrabant , Nahid Jamshidi

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…

Dynamical Systems · Mathematics 2008-09-01 Ioana Ciotir , Aurel Rascanu

We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved…

Probability · Mathematics 2007-06-19 Andreas Neuenkirch

In this article, we study the McKean-Vlasov neutral stochastic differential delay equations driven by fractional Brownian motion with super-linearly growing coefficients, where the Hurst exponent $H\in(1/2,1)$. The existence and uniqueness…

Probability · Mathematics 2025-10-28 Li Tan , Shizhong Hu , Shengrong Wang

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

We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the…

Probability · Mathematics 2025-08-15 Jinlong Wei , Junhao Hu , Guangying Lv , Chenggui Yuan

We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the…

Optimization and Control · Mathematics 2017-07-10 Rainer Buckdahn , Shuai Jing

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence…

Probability · Mathematics 2016-11-29 Jiaqiang Wen , Yufeng Shi

In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to…

Probability · Mathematics 2024-10-02 Johanna Garzon , Jorge A. Leon , Soledad Torres , Ciprian A. Tudor , Lauri Viitasaari

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter $\hat{\cal H} \in ( 1/2, 1)$. Using fixed point techniques, a…

Optimization and Control · Mathematics 2023-01-24 Naima Hakkar , Rajesh Dhayal , Amar Debbouche , Delfim F. M. Torres

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

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of…

Probability · Mathematics 2012-06-18 Yuliya Mishura , Georgiy Shevchenko