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We study the existence of a unique solution to semilinear fractional backward doubly stochastic differential equation driven by a Brownian motion and a fractional Brownian motion with Hurst parameter less than 1/2. Here the stochastic…

Probability · Mathematics 2010-05-13 Shuai Jing , Jorge León

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

Two discretizations of a class of locally Lipschitz Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel…

Probability · Mathematics 2014-08-21 Plamen Turkedjiev

In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the existence and uniqueness of solutions of backward stochastic…

Probability · Mathematics 2024-10-10 Xuan Liu , Zhongmin Qian

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

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel's martingales and an independent multi-dimensional Brownian motion, where Teugel's martingales are a family of pairwise…

Optimization and Control · Mathematics 2011-01-11 Maoning Tang , Qi Zhang

In this paper, we consider forward-backward stochastic differential equation driven by $G$-Brownian motion ($G$-FBSDEs in short) with small parameter $\varepsilon > 0$. We study the asymptotic behavior of the solution of the backward…

Probability · Mathematics 2020-03-27 Ibrahim Dakaou , Abdoulaye Soumana Hima

In this paper, we consider a class of backward doubly stochastic differential equations (BDSDE for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the…

Probability · Mathematics 2017-02-06 Yaozhong Hu , David Nualart , Xiaoming Song

The present paper considers a new kind of backward stochastic differential equations driven by G-Brownian motion, which is called ergodic G-BSDEs. Firstly, the well-posedness of G-BSDEs with infinite horizon is given by a new linearization…

Probability · Mathematics 2017-01-13 Mingshang Hu , Falei Wang

In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and…

Probability · Mathematics 2019-06-19 Dong Cao , Shanjian Tang

Backward stochastic differential equations (BSDEs) appear in numeruous applications. Classical approximation methods suffer from the curse of dimensionality and deep learning-based approximation methods are not known to converge to the BSDE…

Probability · Mathematics 2022-04-20 Martin Hutzenthaler , Tuan Anh Nguyen

In this paper we address again the problem of the connection between multitime Brownian sheet and heat type PDEs. The main results include: the volumetric character of the solutions of the forward (backward) diffusion-like PDEs; the forward…

Probability · Mathematics 2011-12-14 Constantin Udriste , Virgil Damian , Ionel Tevy

This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the…

Probability · Mathematics 2025-07-08 Wenbo Wang , Guangyan Jia

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

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…

Probability · Mathematics 2018-05-23 Soukaina Douissi , Jiaqiang Wen , Yufeng Shi

We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite…

Mathematical Finance · Quantitative Finance 2026-01-06 Miryana Grigorova , James Wheeldon

In this paper, we study the Backward stochastic Volterra integral equation driven by G-Brownian motion (G-BSVIE). By adopting a different backward iteration method, we construct the approximating sequences on each local interval. With the…

Probability · Mathematics 2025-12-30 Bingru Zhao , Mingshang Hu

We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the…

Probability · Mathematics 2017-03-10 Hao Xing , Gordan Žitković

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is…

Probability · Mathematics 2020-08-26 Giulia Di Nunno , Yuliya Mishura , Kostiantyn Ralchenko

We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process $X$ with values in a space of continuous functions $\mathbf C$, with…

Probability · Mathematics 2013-04-10 Marco Fuhrman , Federica Masiero , Gianmario Tessitore