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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

We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a sense related to random dynamical systems. This type of…

Probability · Mathematics 2025-02-25 Nicolas Marie , Paul Raynaud de Fitte

In this work we study rough differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4 and establish Varadhan's small time estimates for the density of solutions of such equations under Hormander's type…

Probability · Mathematics 2013-04-30 Fabrice Baudoin , Cheng Ouyang , Xuejing Zhang

In the paper, Harnack inequalities are established for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H<1/2$. As applications, strong Feller property, log-Harnack inequality and entropy-cost…

Probability · Mathematics 2012-02-17 Xi-Liang Fan

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

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with H\"older regularity greater than 1/4. After recalling how to treat the case of ordinary…

Probability · Mathematics 2009-01-15 Samy Tindel , Iván Torrecilla

In this note we consider stochastic differential equations driven by fractional Brownian motions (fBm) with Hurst parameter $H>1/3$. We prove that the corresponding modified Euler scheme and its Malliavin derivatives are integrable,…

Probability · Mathematics 2023-07-14 Jorge León , Yanghui Liu , Samy Tindel

Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less…

Statistics Theory · Mathematics 2024-12-10 Trisha Maitra , Sourabh Bhattacharya

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the…

Probability · Mathematics 2019-03-07 Jan Gairing , Peter Imkeller , Radomyra Shevchenko , Ciprian A. Tudor

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

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

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

Numerical Analysis · Mathematics 2015-03-13 Jiarui Yang , Jinqiao Duan

We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate,…

Probability · Mathematics 2009-05-12 Es-Sebaiy Khalifa , Idir Ouassou , Youssef Ouknine

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

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The…

Probability · Mathematics 2010-03-09 Mireia Besalú , Carles Rovira

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 paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter $H\in (0,1)\setminus \{\frac12\}$. We show that, for…

Probability · Mathematics 2016-01-20 Christian Bender , Lauri Viitasaari

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

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized…

Probability · Mathematics 2024-04-05 Ercan Sönmez

In this paper, we investigate the regularities for a class of distribution dependent SDEs driven by two independent fractional noises $B^H$ and $\ti B^{\ti H}$ with Hurst parameters $H\in(0,1)$ and $\ti H\in(1/2,1)$. We establish the…

Probability · Mathematics 2023-04-04 Xiliang Fan , Xing Huang , Zewei Ling