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This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao and Liu \cite{GL}, this extends the corresponding results collected in…

Probability · Mathematics 2014-07-22 Jin Ma , Zhenjie Ren , Nizar Touzi , Jianfeng Zhang

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

The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty…

Probability · Mathematics 2025-01-08 Xiaoxiao Peng , Shijie Zhou , Wei Lin , Xuerong Mao

In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.

Probability · Mathematics 2017-03-01 Amel Redjil , Salah Eddine Choutri

We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…

Probability · Mathematics 2011-03-18 Shuai Jing

In this paper, we study the multi-dimensional reflected backward stochastic differential equation driven by $G$-Brownian motion ($G$-BSDE) with a multi-variate constraint on the $G$-expectation of its solution. The generators are diagonally…

Probability · Mathematics 2024-07-26 Yiqing Lin , Falei Wang , Hui Zhao

In this paper, we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise. The main difficulties come from the highly non-linear coefficient. Here we adopt a new sufficient…

Probability · Mathematics 2021-11-17 Ran Wang , Beibei Zhang

In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential…

Probability · Mathematics 2019-03-18 Yongqiang Suo , Chenggui Yuan

The aim is to prove the well-posedness of infinite horizon backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with quadratic generators. To this end, we provide a full construction of explicit solutions to…

Probability · Mathematics 2025-09-09 Yiqing Lin , Yifan Sun , Falei Wang

In this paper, we study the backward stochastic differential equations driven by G-Brownian motion with double mean reflections, which means that the constraints are made on the law of the solution. Making full use of the backward Skorokhod…

Probability · Mathematics 2024-05-16 Wei He , Hanwu Li

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…

Probability · Mathematics 2025-12-12 Huijie Qiao

In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first…

Probability · Mathematics 2025-03-21 Hanwu Li , Ning Ning

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.

Probability · Mathematics 2015-10-07 Yiqing Lin , Xuepeng Bai

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $\sigma:\rr^d\to…

Probability · Mathematics 2026-04-14 Yutao ma , Ran Wang , Liming Wu

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

Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…

Numerical Analysis · Mathematics 2025-09-09 Daili Sheng , Minghui Song , Xiang Peng , Xuanqi Dong

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…

Probability · Mathematics 2014-04-08 Yunjiao Hu , Guangqiang Lan

In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via…

Probability · Mathematics 2025-08-27 Wei He , Qiangjun Tang

In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…

Probability · Mathematics 2022-12-27 Ananta K Majee

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…

Probability · Mathematics 2025-09-16 Wenting Xu , Yong Xu , Xiaoyu Yang , Bin Pei