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Related papers: Moderate deviations for fully coupled multiscale w…

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In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…

Probability · Mathematics 2017-06-02 Matthew R. Morse , Konstantinos Spiliopoulos

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

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…

Statistics Theory · Mathematics 2023-06-26 Chiara Amorino , Akram Heidari , Vytautė Pilipauskaitė , Mark Podolskij

Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…

Probability · Mathematics 2016-10-12 Stefano Favaro , Shui Feng , Fuqing Gao

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

Probability · Mathematics 2014-10-17 Markus Fischer

In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…

Analysis of PDEs · Mathematics 2024-07-08 Jinhuan Wang , Mengdi Zhuang , Hui Huang

We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular setting, numerical evidence suggests that the particles…

Probability · Mathematics 2025-02-19 Zachary P. Adams , Maximilian Engel , Rishabh S. Gvalani

We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…

Analysis of PDEs · Mathematics 2025-05-13 François Delarue , Alvin Tse

We study a sequential system of interacting diffusions in which particle $i$ interacts only with its predecessors through the empirical measure $\mu_t^{i-1}$, yielding a directed, non-exchangeable mean-field approximation of a…

Probability · Mathematics 2026-02-03 Zhenfu Wang , Xianliang Zhao

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

Probability · Mathematics 2025-09-30 Jie Xiang , Huijie Qiao

We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…

Probability · Mathematics 2016-03-31 Amarjit Budhiraja , Eric Friedlander

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

Analysis of PDEs · Mathematics 2021-08-09 Julien Barré , Cedric Bernardin , Raphaël Chétrite , Yash Chopra , Mauro Mariani

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…

Probability · Mathematics 2019-05-02 Wenqing Hu , Michael Salins , Konstantinos Spiliopoulos

The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…

Analysis of PDEs · Mathematics 2024-06-19 Li Chen , Paul Nikolaev , David J. Prömel

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 establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that,…

Probability · Mathematics 2017-03-01 Augusto Almeida Santos , Soummya Kar , José M. F. Moura , João Xavier

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

This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying…

Probability · Mathematics 2024-06-18 Zhang Chen , Bixiang Wang

The term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak…

Probability · Mathematics 2022-02-01 Luisa Beghin , Claudio Macci

The goal of this paper is to approximate several kinds of {\it Mckean-Vlasov SDEs} with {\it irregular coefficients} via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme…

Probability · Mathematics 2019-06-06 Jianhai Bao , Xing Huang