Law of large numbers for a general system of stochastic differential equations with global interaction
type: Item
instance of: scholarly article
title: Law of large numbers for a general system of stochastic differential equations with global interaction
zbMATH Open document ID: 0783.60053
DOI: 10.1016/0304-4149(93)90089-M
author: William Finnoff
published in: Stochastic Processes and their Applications
publication date: 1994-03-14T00:00:00Z
review text: A law of large numbers in the form of the weak convergence of the empirical measures on trajectories of processes forming a triangular array is deduced. Then \(n\) processes in the \(n\)th line of the array are given as the solutions of a system of ordinary stochastic differential equations derived by semimartingales with a special (``mean field'') interaction. The limit is described as the solution of another stochastic differential equation. The model is motivated consisely by possible applications in economy. The proofs are based on a special discrete time approximation of the array of processes, nontrivial estimates, and stability results of J. Jacod and J. Memin.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 203261
zbMATH Keywords: interacting stochastic processes
zbMATH Keywords: law of large numbers
zbMATH Keywords: discrete time approximation
zbMATH Keywords: weak convergence of the empirical measures
zbMATH Keywords: ordinary stochastic differential equations
zbMATH Keywords: semimartingales
reviewed by: Petr Holický
MaRDI profile type: Publication
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full work available at URL: 0304-4149(93)90089-m
OpenAlex ID: W2032353807
description: scientific article; zbMATH DE number 203261