Large Deviation Properties of Weakly Interacting Processes via Weak Convergence Methods

Abstract

We study large deviation properties of systems of weakly interacting particles modeled by It stochastic differential equations (SDEs).It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends toinfinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergenceapproach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2010
Accession Number
AD1135462

Entities

People

  • Amarjit Budhiraja
  • M. Fischer
  • P. Dupuis

Organizations

  • University of North Carolina

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Brownian Motion
  • Computational Fluid Dynamics
  • Differential Equations
  • Diffusion Coefficient
  • Equations
  • Filtration
  • Lyapunov Functions
  • Mathematics
  • Navier Stokes Equations
  • New York
  • Operations Research
  • Partial Differential Equations
  • Probabilistic Models
  • Probability
  • Random Variables
  • Statistics
  • Stochastic Control
  • Stochastic Processes
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.