English
Related papers

Related papers: A uniqueness theorem for solution of BSDEs

200 papers

In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…

Probability · Mathematics 2022-08-09 Yufeng Shi , Zhi Yang

We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$,…

Probability · Mathematics 2019-10-21 Shengjun Fan , Ying Hu

We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…

Probability · Mathematics 2025-03-17 Wenbo Wang , Guangyan Jia

This paper is devoted to the $L^p$ ($p>1$) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in $t$ and $\omega$. An…

Probability · Mathematics 2016-03-02 Yajun Liu , Depeng Li , Shengjun Fan

In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…

Probability · Mathematics 2015-05-19 A. Matoussi , Lambert Piozin , A. Popier

By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^1$ solutions of multidimensional backward stochastic differential equations (BSDEs)…

Probability · Mathematics 2025-09-16 Yuru Lai , Xinying Li , Shengjun Fan

We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator $g$ has an iterated-logarithmic uniform continuity in the…

Probability · Mathematics 2023-07-24 Shengjun Fan , Ying Hu , Shanjian Tang

A Backward Stochastic Differential Equation (BSDE) with a Peano-type generator, is known to have infinitely many solutions when the terminal value is vanishing, and is shown to have possibly multiple solutions even when the terminal value…

Probability · Mathematics 2025-10-27 Shengjun Fan , Ying Hu , Shanjian Tang

In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-integrable with the positive parameter…

Probability · Mathematics 2018-05-17 Rainer Buckdahn , Ying Hu , Shanjian Tang

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…

Probability · Mathematics 2024-04-17 Guang Yang

In this paper, we study the uniqueness of the solution of reflected BSDE with one or two barriers, under continuous and linear increasing condition of generator $g$. Before that we study the construction of solution of of reflected BSDE…

Symplectic Geometry · Mathematics 2008-01-25 G. Jia , Mingyu Xu

In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the…

Probability · Mathematics 2012-06-04 Na Zhang , Guangyan Jia

In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we…

Probability · Mathematics 2021-11-16 Yuyang Chen , Peng Luo

In this paper, we study backward stochastic differential equations driven by a G-Brownian motion. The solution of such new type of BSDE is a triple (Y,Z,K) where K is a decreasing G-martingale. Under a Lipschitz condition for generator f…

Probability · Mathematics 2012-06-27 Mingshang Hu , Shaolin Ji , Shige Peng , Yongsheng Song

In this paper, we study the well-posedness of backward doubly stochastic differential equations (BDSDEs), both with and without reflection, under weak conditions. First, when the generator $f$ is of general growth in $y$ and linear growth…

Probability · Mathematics 2026-03-17 Shuxian Gao , Ying Hu , Jiaqiang Wen

This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect to both unknown variables $y$ and $z$) in a…

Probability · Mathematics 2021-07-28 Shengjun Fan , Ying Hu , Shanjian Tang

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

This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…

Probability · Mathematics 2015-08-12 ShengJun Fan

A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…

Probability · Mathematics 2010-06-08 Yufeng Shi , Qingfeng Zhu

In this paper, we focus on the solvability of a class of fractional backward stochastic differential equations (BSDEs, for short) with delayed generator. In this class of equations, the generator includes not only the values of the…

Probability · Mathematics 2022-12-01 Jiaqiang Wen