Accession Number : AD1050643

Title :   Theory and Applications of Weakly Interacting Markov Processes

Descriptive Note : Technical Report,21 Jul 2014,19 Oct 2017

Corporate Author : University of North Carolina - Chapel Hill Chapel Hill United States

Personal Author(s) : Budhiraja,Amarjit

Full Text :

Report Date : 03 Feb 2018

Pagination or Media Count : 30

Abstract : Systems modeled by a large number of dynamic interacting particles have long been of interest in Statistical Physics. In recent years similar models have started appearing in many other fields as well. These include, communication systems (e.g. loss network models, random medium access protocols), mathematical finance (e.g. mean field games, default clustering in large portfolios), chemical and biological systems( e.g. biological aggregation, chemotactic response dynamics), neuroscience and social sciences (e.g. opinion dynamics models.) The objective of this project is to develop mathematical theory that enables to predict the behavior of the system when the number of particles is very large, with reliable error bounds, particularly when the system is in steady state. The mathematical results that we are interested in take the form of Law of large numbers and Central Limit Theorems.

Descriptors :   stochastic control , partial differential equations , computer networks , weak convergence , probability , algorithms , brownian motion , communication systems , random variables , systems biology , operations research , lyapunov functions , markov processes

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE