English
Related papers

Related papers: McKean-Vlasov limit for interacting systems with s…

200 papers

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…

Probability · Mathematics 2013-03-14 Tomoyuki Ichiba , Mykhaylo Shkolnikov

We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise…

Probability · Mathematics 2019-09-04 Roberto I. Oliveira , Guilherme Reis

The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…

Probability · Mathematics 2015-10-13 Marie-Noémie Thai

We study 1-Wasserstein propagation of chaos for "McKean-type" nonlinear Markov chains and their associated interacting particle systems. This paper is organized into two parts: the first part combines arguments from various areas of…

Probability · Mathematics 2026-02-10 James Vuckovic

Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a…

Probability · Mathematics 2020-02-28 Sima Mehri , Michael Scheutzow , Wilhelm Stannat , Bijan Z. Zangeneh

The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…

Probability · Mathematics 2023-02-15 Louis-Pierre Chaintron , Antoine Diez

We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Probability · Mathematics 2024-10-10 Louis-Pierre Chaintron

A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…

Probability · Mathematics 2024-08-13 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

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 the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…

Probability · Mathematics 2013-01-25 Vivek S. Borkar , Rajesh Sundaresan

We study the convergence of $N-$particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending…

Probability · Mathematics 2021-03-09 Xavier Erny , Eva Löcherbach , Dasha Loukianova

This work focus on the large deviation principle for a two-time scale McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system.…

Probability · Mathematics 2024-01-02 Xiaoyu Yang , Yong Xu

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

Probability · Mathematics 2025-01-07 Lei Li , Yuelin Wang , Yuliang Wang

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

In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…

Probability · Mathematics 2014-09-04 Samuel Herrmann , Julian Tugaut

We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the $N$-particle distribution and the expected limit which solves the corresponding Vlasov…

Analysis of PDEs · Mathematics 2015-11-13 Pierre-Emmanuel Jabin , Zhenfu Wang

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…

Dynamical Systems · Mathematics 2025-05-30 Cecilia González-Tokman , Joshua Peters

This paper focus on investigating the explicit rate of convergence for the propagation of chaos, in a pathwise sense a family of interacting stochastic particle related to some Brownian driven McKean-Vlasov dynamics. Precisely the McKean…

Probability · Mathematics 2019-07-23 Jean-Francois Jabir

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

Probability · Mathematics 2026-05-14 Sayan Banerjee , Andrew Nguyen