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Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…

Probability · Mathematics 2014-07-03 Eric Luçon , Wilhelm Stannat

We prove a large deviation principle on path space for a class of discrete time Markov processes whose state space is the intersection of a regular domain $\L\subset \R^d$ with some lattice of spacing $\e$. Transitions from $x$ to $y$ are…

Probability · Mathematics 2007-05-23 Anton Bovier , Veronique Gayrard

We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…

Probability · Mathematics 2016-01-18 Insuk Seo

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…

Probability · Mathematics 2022-10-07 Erhan Bayraktar , Suman Chakraborty , Ruoyu Wu

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…

Probability · Mathematics 2025-08-05 Yuhang Jiang , Jinming Li , Shihu Li

We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness…

Probability · Mathematics 2024-09-12 Julien Claisse , Jiazhi Kang , Xiaolu Tan

We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the…

Risk Management · Quantitative Finance 2012-08-31 Josselin Garnier , George Papanicolaou , Tzu-Wei Yang

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…

Probability · Mathematics 2015-04-23 Konstantinos Spiliopoulos

The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by L{\'e}vy processes on $\mathbb{R}^d$ having a finite moment of order $\beta \in [1,2]$ and under standard Lipschitz assumptions on the…

Probability · Mathematics 2025-04-24 Thomas Cavallazzi

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under…

Probability · Mathematics 2025-09-30 Huijie Qiao

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

Probability · Mathematics 2010-12-14 Magdalena Kobylanski

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

Optimization and Control · Mathematics 2024-06-21 Aneel Tanwani , Olga Yufereva

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

Functional Analysis · Mathematics 2018-03-13 Richard C. Kraaij

We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…

Analysis of PDEs · Mathematics 2024-09-18 Christian Kuehn , Tobias Wöhrer

We construct an importance sampling method for computing statistics related to rare events for weakly interacting diffusions. Standard Monte Carlo methods behave exponentially poorly with the number of particles in the system for such…

Probability · Mathematics 2023-11-17 Zachary Bezemek , Max Heldman

The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…

Statistical Mechanics · Physics 2021-08-05 Guillaume Barraquand , Pierre Le Doussal

We study the $N \to \infty$ limit of the normalized largest component in some systems of $N$ diffusive particles with mean-field interaction. By applying a universal time change, the interaction in noises is transferred to the drift terms,…

Probability · Mathematics 2024-01-17 Nikolaos Kolliopoulos , David Sanchez , Amy Xiao

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift…

Probability · Mathematics 2025-11-25 Zhaohang Wang , Junhao Hu , Chenggui Yuan

We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…

Optimization and Control · Mathematics 2025-12-02 Julien Claisse , Jiazhi Kang , Tianxu Lan , Xiaolu Tan

The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct…

Probability · Mathematics 2020-06-03 Meiqi Liu , Huijie Qiao