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In this paper, we study the problem of Poisson stability of solutions for stochastic semi-linear evolution equation driven by fractional Brownian motion \mathrm{d} X(t)= \left( AX(t) + f(t, X(t)) \right) \mathrm{d}t + g\left(t,…

Dynamical Systems · Mathematics 2024-10-22 Xinze Zhang , Li Yong , Xue Yang

In this article, we study the stability of solutions to 3D stochastic primitive equations driven by fractional noise. Since the fractional Brownian motion is essentially different from Brownian motion, lots of stochastic analysis tools are…

Probability · Mathematics 2021-04-21 Lidan Wang , Guoli Zhou

In this paper, we study the mean-square stability of the solution and its stochastic theta scheme for the following stochastic differential equations drive by fractional Brownian motion with Hurst parameter $H\in (\frac 12,1)$: $$…

Numerical Analysis · Mathematics 2021-09-21 Min Li , Yaozhong Hu , Chengming Huang , Xiong Wang

In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…

Probability · Mathematics 2025-05-01 Li Tan , 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

In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…

Probability · Mathematics 2026-01-12 Amjad Saef , Wilhelm Stannat

We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…

Probability · Mathematics 2025-12-23 Konstantinos Dareiotis , El Mehdi Haress , Khoa Lê

We study a rough differential equation driven by fractional Brownian motion with Hurst parameter $H$ $(1/4<H \le 1/2)$. Under H\"ormander's condition on the coefficient vector fields, the solution has a smooth density for each fixed time.…

Probability · Mathematics 2019-09-12 Yuzuru Inahama , Nobuaki Naganuma

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…

Numerical Analysis · Mathematics 2017-09-18 Guang-an Zou , Guangying Lv , Jiang-Lun Wu

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

We study the asymptotic expansions with respect to $h$ of \[\mathrm{E}[\Delta_hf(X_t)],\qquad \mathrm{E}[\Delta_hf(X_t)|\mathscr{F}^X_t]\quadand\quad \mathrm{E}[\Delta_hf(X_t)|X_t],\] where $\Delta_hf(X_t)=f(X_{t+h})-f(X_t)$, when…

Probability · Mathematics 2009-09-29 Sébastien Darses , Ivan Nourdin

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…

Probability · Mathematics 2007-05-23 Martin Hairer

We first introduce the calculus of Peng's G-Brownian motion on a sublinear expectation space $(\Omega, {\cal H}, \hat{\mathbb{E}})$. Then we investigate the exponential stability of paths for a class of stochastic differential equations…

Probability · Mathematics 2013-12-02 Weiyin Fei , Chen Fei

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…

Dynamical Systems · Mathematics 2013-02-11 Yajing Li , Yejuan Wang

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 show that under some assumptions, for a $d$-dimensional fractional Brownian motion with Hurst parameter $H>1/2$, the density of solution of stochastic differential equation driven by it has a short-time expansion similar to…

Probability · Mathematics 2010-05-20 Fabrice Baudoin , Cheng Ouyang

In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…

Probability · Mathematics 2016-02-29 Qiong Wu

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

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 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