Theory and Applications of Weakly Interacting Markov Processes

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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 03, 2018
Accession Number
AD1050643

Entities

People

  • Amarjit Budhiraja

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Communication Systems
  • Computational Science
  • Computer Networks
  • Differential Equations
  • Diffusion Coefficient
  • Equations
  • Lyapunov Functions
  • Markov Chains
  • Markov Processes
  • Operations Research
  • Partial Differential Equations
  • Random Variables
  • Social Sciences
  • Stochastic Control
  • Stochastic Processes
  • Systems Biology

Fields of Study

  • Mathematics

Readers

  • Agent-Based Social Robotics and Mobile-Assisted Learning in Virtual Environments.
  • Computational Modeling and Simulation
  • Statistical inference.