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We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differential equation that models small random perturbations of a…

Probability · Mathematics 2019-10-21 Wenqing Hu , Chris Junchi Li , Xiang Zhou

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that $t\to X_t$ is a Markov process and we wish to calculate the measure-valued process…

Probability · Mathematics 2007-05-23 Michael A. Kouritzin , Wei Sun

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…

Methodology · Statistics 2024-11-12 Ajay Jasra , Mohamed Maama , Raul Tempone

Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic…

Probability · Mathematics 2025-03-31 Noufel Frikha , Xuanye Song

We develop an Euler-type particle method for the simulation of a McKean--Vlasov equation arising from a mean-field model with positive feedback from hitting a boundary. Under assumptions on the parameters which ensure differentiable…

Numerical Analysis · Mathematics 2018-05-31 Vadim Kaushansky , Christoph Reisinger

We analyze a data-processing system with $n$ clients producing jobs which are processed in \textit{batches} by $m$ parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup…

Performance · Computer Science 2020-09-22 Sounak Kar , Robin Rehrmann , Arpan Mukhopadhyay , Bastian Alt , Florin Ciucu , Heinz Koeppl , Carsten Binnig , Amr Rizk

We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…

Analysis of PDEs · Mathematics 2026-05-05 Nadia Khoury , P. -E. Jabin

Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…

Numerical Analysis · Mathematics 2020-08-04 Ruisheng Qi , Xiaojie Wang

We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field limit of interacting particle systems with singular…

Probability · Mathematics 2024-04-09 Jiawei Li , Zhongmin Qian

We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…

Statistical Mechanics · Physics 2009-11-13 Carlos E. Fiore , Mário J. de Oliveira

The paper has two objectives: proving that the rate of convergence in distribution for mean-field models in CLT regime is $N^{-1/2}$, and obtaining explicit expressions for the infinitesimal generators of two types of measure-valued Markov…

Probability · Mathematics 2025-02-05 Xavier Erny

In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…

Data Analysis, Statistics and Probability · Physics 2015-01-08 J. Li , P. Vignal , S. Sun , V. M. Calo

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like…

Quantum Physics · Physics 2023-10-10 Navneeth Ramakrishnan , Marco Tomamichel , Mario Berta

In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…

Computation · Statistics 2015-10-19 Ajay Jasra , Kengo Kamatani , Kody J. H. Law , Yan Zhou

In this paper, an initial error tolerant distributed mean field control method under partial and discrete information is introduced, where each agent only has discrete observations on its own state. First, we study agents' behavior in…

Optimization and Control · Mathematics 2026-01-23 Yuxin Jin , Haotian Wang , Wang Yao , Xiao Zhang

Chemotaxis models describe the movement of organisms in response to chemical gradients. In this paper, we present a stochastic interacting particle-field algorithm with a random batch approximation (SIPF-$r$) for the three-dimensional (3D)…

Numerical Analysis · Mathematics 2026-01-26 Boyi Hu , Zhongjian Wang , Jack Xin , Zhiwen Zhang

We consider a system of $N$ Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable $N$-particle distribution. In this…

Probability · Mathematics 2025-05-13 Armand Bernou , Mitia Duerinckx , Matthieu Ménard

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Probability · Mathematics 2020-07-02 Jasper Hoeksema , Thomas Holding , Mario Maurelli , Oliver Tse

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 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