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The main goal of this article is to derive a two-sided estimate for hitting probabilities of a hypoelliptic stochastic differential equation (SDE) driven by fractional Brownian motion (fBM) with Hurst parameter $H\in(1/4,1)$ in terms of…

Probability · Mathematics 2025-12-09 Xi Geng , Sheng Wang

Distribution dependent stochastic differential equations have been a very hot subject with extensive studies. On the other hand, under the $G$-expectation framework, stochastic differential equations driven by $G$-Brownian motion (in short…

Probability · Mathematics 2023-02-27 De Sun , Jiang-Lun Wu , Panyu Wu

This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…

Probability · Mathematics 2023-05-24 Pei Zhang , Nur Anisah Mohamed , Adriana Irawati Nur Ibrahim

Let $B^{H}$ be a $d$-dimensional fractional Brownian motion with Hurst index $H\in(0,1)$, $f:[0,1]\longrightarrow\mathbb{R}^{d}$ a Borel function, and $E\subset[0,1]$, $F\subset\mathbb{R}^{d}$ are given Borel sets. The focus of this paper…

Probability · Mathematics 2023-06-21 Mohamed Erraoui , Youssef Hakiki

We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…

Probability · Mathematics 2024-11-08 Mazyar Ghani Varzaneh , Sebastian Riedel

We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary…

Probability · Mathematics 2020-03-12 Karine Bertin , Nicolas Klutchnikoff , Fabien Panloup , Maylis Varvenne

In this note we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter $H > 1/2$. Then, we show that, when the delay…

Probability · Mathematics 2009-04-01 Marco Ferrante Carles Rovira

The strong convergence rate of the Euler scheme for SDEs driven by additive fractional Brownian motions is studied, where the fractional Brownian motion has Hurst parameter $H\in(\frac13,\frac12)$ and the drift coefficient is not required…

Numerical Analysis · Mathematics 2022-01-19 Chuying Huang , Xu Wang

In this paper, we establish the propagation of chaos and Euler-Maruyama method of DDSDE driven by multiplicative fractional Brownian motion with Hurst parameter $H\in (\frac{\sqrt{5}-1}{2},1)$. We have not only obtained an upper bound for…

Probability · Mathematics 2025-12-22 Guangjun Shen , Jiangpeng Wang , Xuekang Zhang

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…

Probability · Mathematics 2016-10-05 Aurélien Deya , Fabien Panloup , Samy Tindel

Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H \in (1/3, 1/2]$.

Probability · Mathematics 2024-08-27 Francesco C. De Vecchi , Luca M. Giordano , Daniela Morale , Stefania Ugolini

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

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…

Probability · Mathematics 2016-07-25 Johanna Garzón , Jorge A. León , Soledad Torres

In this paper we are concerned with distribution dependent backward stochastic differential equations (DDBSDEs) driven by Gaussian processes. We first show the existence and uniqueness of solutions to this type of equations. This is done by…

Probability · Mathematics 2023-02-08 Xiliang Fan , Jiang-Lun Wu

In this paper, we study the recovery of the Hurst parameter from a given discrete sample of fractional Brownian motion with statistical inverse theory. In particular, we show that in the limit the posteriori distribution of the parameter…

Probability · Mathematics 2020-02-25 Lassi Päivärinta , Petteri Piiroinen

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

We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…

Probability · Mathematics 2011-12-13 Yuriy Kozachenko , Alexander Melnikov , Yuliya Mishura

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

In this work, we investigate the existence and properties of Gaussian-like densities for weak solutions of multidimensional stochastic differential equations driven by a mixture of completely correlated fractional Brownian motions. We…

Probability · Mathematics 2025-03-06 Maximilian Buthenhoff , Ercan Sönmez

In this work, we prove a version of H\"{o}rmander's theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent $\frac{1}{2} < H < 1$ and an analytic semigroup on a given separable…

Probability · Mathematics 2020-03-19 Jorge A. de Nascimento , Alberto Ohashi