English
Related papers

Related papers: Linear Stochastic Differential Equations Driven by…

200 papers

We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…

Probability · Mathematics 2020-06-18 Amarjit Budhiraja , Xiaoming Song

In this study, we develop a new theory of estimating Hurst parame- ter using conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solution of stochastic differentional equations (SDEs) driven by…

In this paper, our main aim is to investigate the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in(1/2, 1)$. After giving…

Numerical Analysis · Mathematics 2024-10-01 Shengrong Wang , Jie Xie , Li Tan

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

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

We derive estimates for the solutions to differential equations driven by a H\"older continuous function of order $\beta>1/2$. As an application we deduce the existence of moments for the solutions to stochastic partial differential…

Probability · Mathematics 2007-05-23 Yaozhong Hu David Nualart

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

In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H\in(1/2,1). We prove the well-posedness of this type equations, and then establish a…

Probability · Mathematics 2021-06-01 Xiliang Fan , Xing Huang , Yongqiang Suo , Chenggui Yuan

We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2.…

Probability · Mathematics 2025-12-16 Antoine-Marie Bogso , Olivier Menoukeu Pamen , Frank Proske

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…

Numerical Analysis · Mathematics 2020-06-08 Yanzhao Cao , Jialin Hong , Zhihui Liu

In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2019-04-23 Jian Song , Xiaoming Song , Fangjun Xu

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…

Chaotic Dynamics · Physics 2013-09-26 Jinzhi Lei , Michael C. Mackey

We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…

Probability · Mathematics 2011-03-18 Shuai Jing

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 study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…

Probability · Mathematics 2007-05-23 Fabrice Baudoin , David Nualart

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

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the…

Probability · Mathematics 2007-05-23 Laure Coutin , Peter Friz , Nicolas Victoir

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

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…

Probability · Mathematics 2026-01-12 Saloua Labed , Nacira Agram , Bernt Oksendal

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu