A Law of Large Numbers for an Interacting Particle System with Confining Potential

2007/01/03 by Matteo Ortisi, Ortisi, Matteo
Economics, Econometrics and Finance · Mathematics · #82C22 #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.math/0701095

openalex publication_date 2007/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction potential modeling the interaction among all the particles of the system. The limiting behavior as the size N grows to infinity is achieved as a law of large numbers for the empirical process associated with the interacting particle system

Citations

• Large deviations, free energy functional and quasi-potential for a mean field model of interacting diffusions

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