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This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…

Analysis of PDEs · Mathematics 2021-08-26 Noufel Frikha , Paul-Eric Chaudru de Raynal

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Probability · Mathematics 2022-03-24 Mathieu Laurière , Ludovic Tangpi

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…

Machine Learning · Statistics 2026-05-15 Ayoub Belhadji , Daniel Sharp , Youssef M. Marzouk

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…

Probability · Mathematics 2012-11-09 Pierre Del Moral , Emmanuel Rio

In this paper, uniform in time quantitative propagation of chaos in $L^1$-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the drift is assumed to…

Probability · Mathematics 2025-10-29 Xing Huang

We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…

Probability · Mathematics 2011-10-25 A. Manita , V. Shcherbakov

The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…

Probability · Mathematics 2022-09-01 Xuda Ye , Zhennan Zhou

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

Probability · Mathematics 2024-03-27 Kai Du , Yunzhang Li , Yuyang Ye

We consider a class of birth-and-death processes describing a population made of $d$ sub-populations of different types which interact with one another. The state space is $\mathbb{Z}_+^d$ (unbounded). We assume that the population goes…

Probability · Mathematics 2018-11-20 J. -R. Chazottes , P. Collet , S. Méléard

Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…

Probability · Mathematics 2018-05-30 Alain Durmus , Andreas Eberle , Arnaud Guillin , Raphael Zimmer

This paper develops a non-asymptotic, local approach to quantitative propagation of chaos for a wide class of mean field diffusive dynamics. For a system of $n$ interacting particles, the relative entropy between the marginal law of $k$…

Probability · Mathematics 2023-05-31 Daniel Lacker

Many low temperature particle systems in mean-field interaction are ergodic with respect to a unique invariant measure, while their (non-linear) mean-field limit may possess several steady states. In particular, in such cases, propagation…

Probability · Mathematics 2025-02-11 Lucas Journel , Pierre Le Bris

The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…

Probability · Mathematics 2024-04-12 Alexander M. G. Cox , Emma Horton , Denis Villemonais

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba

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 $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration…

Probability · Mathematics 2026-01-14 Erhan Bayraktar , Donghan Kim

This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by…

Probability · Mathematics 2021-12-30 Kai Du , Yifan Jiang , Jinfeng Li

We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are applied to multi-dimensional birth and death…

Probability · Mathematics 2018-10-17 Nicolas Champagnat , Denis Villemonais

We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…

Probability · Mathematics 2022-12-20 Pierre Degond , Mario Pulvirenti , Stefano Rossi