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This paper introduces a backward stochastic differential equation driven by both Brownian motion and a Markov chain (BSDEBM). Regime-switching is also incorporated through its driver. The existence and uniqueness of the solution of the…

Probability · Mathematics 2022-03-08 Engel John C. Dela Vega , Robert J. Elliott

Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral…

Analysis of PDEs · Mathematics 2013-05-06 María J. Garrido-Atienza , Kening Lu , Björn Schmalfuss

Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the…

Probability · Mathematics 2017-03-24 Xiaoming Xu

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 obtain existence and uniqueness in L^p, p>1 of the solutions of a backward stochastic differential equations (BSDEs for short) driven by a marked point process, on a bounded interval. We show that the solution of the BSDE can be…

Probability · Mathematics 2016-12-04 Fulvia Confortola

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2019-07-02 Xi Geng , Cheng Ouyang , Samy Tindel

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

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

In this paper, we study the numerical method for solving forward-backward stochastic differential equations driven by $G$-Brownian motion ($G$-FBSDEs) which correspond to fully nonlinear partial differential equations (PDEs). First, we give…

Numerical Analysis · Mathematics 2022-05-19 Mingshang Hu , Lianzi Jiang

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

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional brownian motion and the multifractional…

Probability · Mathematics 2019-12-03 Habiba Knani , Marco Dozzi

In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion (fBm) and a Wiener process and having jumps. We prove that this equation has a unique solution and show that all its moments are finite.

Probability · Mathematics 2013-04-02 Georgiy Shevchenko

We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time $t$ can depend on the values of a solution in the…

Probability · Mathematics 2017-03-31 Badreddine Mansouri , Imen Salhi , Lazhar Tamer

We consider a reflected backward stochastic differential equations with default time and an optional barrier in a filtration generated by a one-dimensional Brownian motion and a defaultable process. We suppose that the barrier have…

Probability · Mathematics 2026-05-07 Badr Elmansouri , Mohamed El Otmani

In this paper, we are concerned with multi-scale distribution dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index $H>\frac12$ and standard Brownian motion, simultaneously. Our aim is to…

Probability · Mathematics 2023-06-12 Shen Gunagjun , Zhou Huan , Wu Jianglun

The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in {\mathbb{R}_{+}\times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older…

Probability · Mathematics 2025-02-06 El Mehdi Haress , Alexandre Richard

The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the…

Probability · Mathematics 2020-12-03 Falei Wang , Guoqiang Zheng

In this paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions…

Probability · Mathematics 2023-04-10 Solesne Bourguin , Thanh Dang , Konstantinos Spiliopoulos

In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the…

Probability · Mathematics 2022-05-20 Mingshang Hu , Shaolin Ji , Xiaojuan Li

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