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Related papers: Mean-Field SDEs driven by $G$-Brownian Motion

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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 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

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

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…

Probability · Mathematics 2025-01-29 Lucio Galeati , Máté Gerencsér

The aim of this paper is to present the analysis for the solutions of nonlinear stochastic functional differential equation driven by G-Brownian motion with infinite delay (G-SFDEwID). Under some useful assumptions, we have proved that the…

Probability · Mathematics 2018-06-12 Faiz Faizullah

We study regularity properties of the unique solution of a mean-field $G$-SDE. More precisely, we consider a mean-field $G$-SDE with square-integrable random initial condition and establish its first and second order Fr\'echet…

Probability · Mathematics 2025-08-12 Karl-Wilhelm Georg Bollweg , Thilo Meyer-Brandis

In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the entire subcritical regime and can be…

Probability · Mathematics 2026-02-26 Jiazhen Gu , Qian Yu

In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under the condition that the generator is time-varying Lipschitz continuous with respect to y and time-varying uniformly continuous with…

Probability · Mathematics 2024-09-26 Bingru Zhao

In this paper, we prove the validity of an averaging principle for multi-valued stochastic differential equations (MSDEs) driven by G-Brownian motion with non-Lipschitz coefficients. The convergence theorem between the solution of the…

Probability · Mathematics 2023-08-09 Min Han , Bin Pei

Based on the classical probability, the stability criteria for stochastic differential delay equations (SDDEs) where their coefficients are either linear or nonlinear but bounded by linear functions have been investigated intensively.…

Optimization and Control · Mathematics 2020-04-29 Chen Fei , Weiyin Fei , Xuerong Mao , Litan Yan

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…

Dynamical Systems · Mathematics 2013-01-22 Yong Xu , Rong Guo , Di Liu , Huiqing Zhang , Jinqiao Duan

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

In this paper we consider a class of {\it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common noises, as well as the general version of the so-called…

Probability · Mathematics 2021-08-10 Rainer Buckdahn , Juan Li , Jin Ma

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 [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…

Probability · Mathematics 2007-11-21 Rainer Buckdahn , Juan Li , Shige Peng

We study the problem of optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of \textit{partial…

Optimization and Control · Mathematics 2017-04-12 Roxana Dumitrescu , Bernt Øksendal , Agnès Sulem

In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…

Probability · Mathematics 2017-02-20 Juan Li

We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong well-posedness under a…

Probability · Mathematics 2021-06-01 Lucio Galeati , Fabian A. Harang , Avi Mayorcas

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic…

Analysis of PDEs · Mathematics 2011-07-21 Benjamin Gess , Wei Liu , Michael Roeckner

In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…

Probability · Mathematics 2025-05-01 Li Tan , Shengrong Wang