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Related papers: BSDEs driven by G-Brownian motion with time-varyin…

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This paper is devoted to the study of the differentiability of solutions to real-valued backward stochastic differential equations (BSDEs for short) with quadratic generators driven by a cylindrical Wiener process. The main novelty of this…

Probability · Mathematics 2008-04-10 Philippe Briand , Fulvia Confortola

We are concerned with the discretization of a solution of a Forward-Backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the…

Probability · Mathematics 2015-03-10 Idris Kharroubi , Thomas Lim

We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness…

Probability · Mathematics 2025-01-28 Badr Elmansouri , Mohamed El Otmani

We obtain a representation theorem for the generators of BSDEs driven by G-Brownian motions, and then we use the representation theorem to get a converse comparison theorem for G-BSDEs and some equivalent results for nonlinear expectations…

Probability · Mathematics 2013-06-11 Kun Heand , Mingshang Hu

In this paper, we introduce $ G $-Bessel processes for a class of $ d $-dimensional $ G $-Brownian motions. Under the condition of dimensionality $ d $, we obtain that the $ G $-Bessel process is the solution of the stochastic differential…

Probability · Mathematics 2025-05-20 Mingshang Hu , Renxing Li

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…

Probability · Mathematics 2019-02-26 Shiqiu Zheng , Gaofeng Zong

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

This paper is dedicated to the analysis of forward backward stochastic differential equations driven by a L{\'e}vy process. We assume that the generator and the terminal condition are path-dependent and satisfy a local Lipschitz condition.…

Probability · Mathematics 2025-10-03 Hannah Geiss , Céline Labart , Adrien Richou , Alexander Steinicke

In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the…

Probability · Mathematics 2013-08-19 Zhonghao Zheng , Xiuchun Bi , Shuguang Zhang

In this paper, we investigate suffcient and necessary conditions for the comparison theorem of neutral stochastic functional differential equations driven by G-Brownian motion (G-NSFDE). Moreover, the results extend the ones in the linear…

Probability · Mathematics 2021-09-17 Fen-Fen Yang , Chenggui Yuan

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence…

Probability · Mathematics 2016-11-29 Jiaqiang Wen , Yufeng Shi

We consider ergodic backward stochastic differential equations, in a setting where noise is generated by a countable state uniformly ergodic Markov chain. We show that for Lipschitz drivers such that a comparison theorem holds, these…

Probability · Mathematics 2012-07-25 Samuel N. Cohen , Ying Hu

In this paper, we study backward stochastic Volterra integral equations of type-I with time delayed generators. Under some condition (small time horizon or a Lipschitz constant), we derive an existence and uniqueness results. Next, with the…

Probability · Mathematics 2021-10-06 Harouna Coulibaly , Auguste Aman

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(p\geq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of…

Probability · Mathematics 2014-04-09 Lishun Xiao , Shengjun Fan , Na Xu

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 a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques,…

Probability · Mathematics 2017-01-17 Lishun Xiao , Shengjun Fan

In this paper, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions…

Probability · Mathematics 2021-03-04 Shiqiu Zheng , Lidong Zhang , Lichao Feng

This article is devoted to study the class of backward stochastic differential equation with delayed generator. We suppose the terminal value and the generator to be $L^{p}$-integrable with $p>1$. We derive a new type of estimation related…

Probability · Mathematics 2021-10-05 Yong Ren , Jean Marc Owo , Auguste Aman

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It\^o's formula. Moreover, we study the solvability of the scalar valued stochastic differential…

Probability · Mathematics 2015-10-07 Yiqing Lin

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