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

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This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…

Systems and Control · Electrical Eng. & Systems 2025-06-18 Shakib Mustavee , Shaurya Agarwal , Arvind Singh

Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…

Probability · Mathematics 2017-01-06 Oussama El Barrimi , Youssef Ouknine

The Brownian force model (BFM) is the mean-field model for the avalanches of an elastic interface slowly driven in a random medium. It describes the spatio-temporal statistics of the velocity field, and, to some extent is analytically…

Statistical Mechanics · Physics 2022-03-23 Pierre Le Doussal

In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting pont is propagated separately using the Time-Dependent Hartree-Fock equation of…

Nuclear Theory · Physics 2015-06-11 Denis Lacroix , Sakir Ayik , Bulent Yilmaz , Kouhei Washiyama

In this paper, we build the equivalence between rough differential equations driven by the lifted $G$-Brownian motion and the corresponding Stratonovich type SDE through the Wong-Zakai approximation. The quasi-surely convergence rate of…

Probability · Mathematics 2020-11-11 Shige Peng , Huilin Zhang

In this paper, we prove that there exists at least one solution for the reflected forward-backward stochastic differential equation driven by G-Brownian motion satisfying the obstacle constraint with monotone coefficients.

Probability · Mathematics 2023-01-10 Bingjun Wang , Hongjun Gao , Mei Li

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a…

Probability · Mathematics 2012-01-30 Rémi Rhodes , Bamba A. Sow

In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…

Probability · Mathematics 2025-07-11 Manh Hong Duong , Grigorios A. Pavliotis , Julian Tugaut

In this paper, we study the existence and uniqueness of solutions to the fully coupled nonlinear forward-backward stochastic differential equations driven by G-Brownian motion. Assuming that the diffusion coefficient $\sigma$ is uniformly…

Probability · Mathematics 2021-04-15 Huan Lu , Yongsheng Song

We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process…

Probability · Mathematics 2015-03-19 Alexander Schnurr

In this paper we consider a class of stochastic differential equations driven by subordinate Brownian motion with Markovian switching. We use Malliavin calculus to study the smoothness of the density for the solution under uniform…

Probability · Mathematics 2017-11-27 Xiaobin Sun , Yingchao Xie

We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an…

Probability · Mathematics 2014-12-05 Maik Gorgens

We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error…

Numerical Analysis · Mathematics 2017-10-25 Mario Hefter , André Herzwurm , Thomas Müller-Gronbach

The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in {\mathbb{R}_{+}\times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older…

Probability · Mathematics 2025-02-06 El Mehdi Haress , Alexandre Richard

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 consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way, following the approach of Gubinelli, we…

Probability · Mathematics 2013-10-24 Andreas Neuenkirch , Ivan Nourdin , Andreas Rößler , Samy Tindel

In this work, we investigate the existence and properties of Gaussian-like densities for weak solutions of multidimensional stochastic differential equations driven by a mixture of completely correlated fractional Brownian motions. We…

Probability · Mathematics 2025-03-06 Maximilian Buthenhoff , Ercan Sönmez

In this paper, we first give the existence and uniqueness theorems for generalized mean-filed delay stochastic differential equations (GMFDSDEs) and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study…

Optimization and Control · Mathematics 2017-08-14 Hancheng Guo , Jie Xiong , Jiayu Zheng

In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of…

Probability · Mathematics 2010-07-26 Zhen-Qing Chen , Kyeong-Hun Kim

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…

Analysis of PDEs · Mathematics 2024-03-20 David M. Ambrose , Megan Griffin-Pickering , Alpár R. Mészáros