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We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…

Probability · Mathematics 2010-08-30 Mykhaylo Shkolnikov

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

Dynamical Systems · Mathematics 2023-05-12 Bixiang Wang

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2023-07-17 Zachary Bezemek , Konstantinos Spiliopoulos

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

Probability · Mathematics 2022-05-24 Shuo Yan

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and…

Probability · Mathematics 2024-02-29 Michele Coghi , Wolfgang Dreyer , Paul Gajewski , Clemens Guhlke , Peter Friz , Mario Maurelli

We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, these systems are described by a McKean-Vlasov process - a…

Numerical Analysis · Mathematics 2015-08-11 L. F. Ricketson

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…

Probability · Mathematics 2019-04-25 Julien Reygner

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

In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…

Probability · Mathematics 2022-07-14 Yun Li , Longjie Xie

We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes…

Probability · Mathematics 2018-02-02 Ben Hambly , Sean Ledger

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

Probability · Mathematics 2020-09-23 Grégoire Ferré , Gabriel Stoltz

A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…

Probability · Mathematics 2023-01-25 Kai Du , Yifan Jiang , Xiaochen Li

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is…

Probability · Mathematics 2022-01-19 Daniel Adams , Gonçalo dos Reis , Romain Ravaille , William Salkeld , Julian Tugaut

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…

Numerical Analysis · Mathematics 2023-05-30 Qian Guo , Jie He , Lei Li

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…

Probability · Mathematics 2016-01-26 Paul Dupuis , Kavita Ramanan , Wei Wu

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

Probability · Mathematics 2019-01-18 Son L. Nguyen , George Yin , Tuan A. Hoang

We introduce a heterogeneous formulation of a contagious McKean-Vlasov system, whose inherent heterogeneity comes from asymmetric interactions with a natural and highly tractable structure. It is shown that this formulation characterises…

Probability · Mathematics 2022-09-28 Zachary Feinstein , Andreas Sojmark

For a Markov process associated with a diffusion type Dirichlet form an upper bound is shown for the law of the finite dimensional distributions of the process. Under some more assumptions on the underlaying space this is also shown for the…

Probability · Mathematics 2009-07-28 Ann-Kathrin Jarecki

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

Probability · Mathematics 2018-03-28 Sayan Banerjee , Amarjit Budhiraja , Michael Perlmutter