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This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…

Probability · Mathematics 2015-03-30 El Hassan Lakhel

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a…

Optimization and Control · Mathematics 2012-11-28 Idris Kharroubi , Thomas Lim

A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps.

Probability · Mathematics 2016-07-25 Matyas Barczy , Zenghu Li , Gyula Pap

We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…

Probability · Mathematics 2025-07-01 Maximilian Buthenhoff , Ercan Sönmez

As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds…

Probability · Mathematics 2009-05-07 Jérémie Unterberger

We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise…

Probability · Mathematics 2018-12-27 Jie Xiong , Jiayu Zheng , Xiaowen Zhou

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 give a new estimate on Stieltjes integrals of H\"older continuous functions and use it to prove an existence-uniqueness theorem for solutions of ordinary differential equations with H\"older continuous forcing. We construct stochastic…

Probability · Mathematics 2007-05-23 Anastasia Ruzmaikina

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 consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…

Probability · Mathematics 2025-10-22 Oleg Butkovsky , Khoa Lê , Leonid Mytnik

We consider the stochastic continuity equation perturbed by a fractional Brownian motion and the drift is allowed to be discontinuous. We show that for almost all paths of the fractional Brownian motion there exists a solution to the…

Probability · Mathematics 2018-06-26 Torstein Nilssen

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske

In this paper we study the controllability results of impulsive neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are…

Probability · Mathematics 2016-02-19 El Hassan Lakhel

A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…

Mathematical Physics · Physics 2011-07-15 Jin Li , Jianhua Huang

We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional…

Probability · Mathematics 2018-03-29 Yuliya Mishura , Kostiantyn Ralchenko , Georgiy Shevchenko

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 work, we will show the existence and uniqueness of the solution to the semi linear stochastic differential equations driven by weighted fractional Brownian motion with delay. We also prove smoothness of the density of the solution…

Probability · Mathematics 2020-12-01 Mahdieh Tahmasebi

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…

Statistics Theory · Mathematics 2020-01-07 Min Dai , Jinqiao Duan , Junjun Liao , Xiangjun Wang

In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…

Probability · Mathematics 2010-07-20 Shaokuan Chen , Shanjian Tang

We derive a Tanaka-type formula for the solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (fBm) with Hurst parameter $H > \frac{1}{2}$. While Tanaka formulas for the fractional Brownian motion itself…

Probability · Mathematics 2025-08-11 Tommi Sottinen , Ercan Sönmez , Lauri Viitasaari