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We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…

Probability · Mathematics 2024-03-04 T. Müller-Gronbach , L. Yaroslavtseva

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic…

Probability · Mathematics 2013-07-26 Qian Lin

We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…

Probability · Mathematics 2025-10-07 Charles-Edouard Bréhier , Ibrahima Faye

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 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 investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…

Dynamical Systems · Mathematics 2023-08-22 Mengyu Cheng , Zhenxin Liu , Michael Röckner

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized…

Probability · Mathematics 2024-04-05 Ercan Sönmez

By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder…

Probability · Mathematics 2020-03-10 Xiaobin Sun , Longjie Xie , Yingchao Xie

In this paper, we consider the reflected backward stochastic differential equations driven by G-Brownian motion (reflected G-BSDEs) whose coefficients satisfy the beta-order Mao's condition. The uniqueness is obtained by some a priori…

Probability · Mathematics 2022-12-26 Hanwu Li

In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators, the $z$ parts of whose $l$-th components only depend on the…

Probability · Mathematics 2020-02-18 Guomin Liu

In this paper, we focus on the mean-field backward stochastic differential equations (BSDEs) driven by a fractional Brownian motion with Hurst parameter H greater then 1/2. First, the existence and uniqueness of these equations are…

Probability · Mathematics 2017-05-30 Jiaqiang Wen , Yufeng Shi

We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two…

Probability · Mathematics 2016-11-04 Parisa Fatheddin , Jie Xiong

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 paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the solution for locally Lipschitz GSDEs is obtained by…

Probability · Mathematics 2014-12-22 Xinpeng Li , Xiangyun Lin , Yiqing Lin

In this paper, we study the uniqueness and existence of solutions of RGSDEs with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover we obtain the comparison theorem for RGSDEs with nonlinear resistance.

Probability · Mathematics 2014-09-24 Peng Luo

Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. In this paper, we will establish an averaging principle for multiscale stochastic linearly…

Dynamical Systems · Mathematics 2017-03-14 Peng Gao , Yong Li

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…

Dynamical Systems · Mathematics 2024-09-20 Mengyu Cheng , Zimo Hao , Xicheng Zhang

In this paper, we show that the integration of a stochastic differential equations driven by G-Brownian motion in R can be reduced to the integration of an ordinary differential equations parametrized by a variable in ({\Omega},F). We study…

Probability · Mathematics 2014-09-02 Peng Luo , Falei Wang

In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward…

Probability · Mathematics 2011-05-24 Defei Zhang

This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying…

Probability · Mathematics 2021-11-12 Bin Pei , Yuzuru Inahama , Yong Xu