On the Construction of Lyapunov Functions for Nonlinear Markov Processes Via Relative Entropy

Abstract

We develop an approach to the construction of Lyapunov functions for the forward equation of a finite state nonlinear Markov process.Nonlinear Markov processes can be obtained as a law of large number limit for a system of weakly interacting processes. The approachexploits this connection and the fact that relative entropy defines a Lyapunov function for the solution of the forward equation for themany particle system. Candidate Lyapunov functions for the nonlinear Markov process are constructed via limits, and verified for certainclasses of models.

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Document Details

Document Type
Technical Report
Publication Date
Jul 13, 2011
Accession Number
AD1135430

Entities

People

  • Markus Fischer
  • Paul Dupuis

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Communication Systems
  • Construction
  • Convergence
  • Dynamics
  • Equations
  • Fokker Planck Equations
  • Free Energy
  • Lyapunov Functions
  • Markov Processes
  • Mathematics
  • Neural Networks
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistics
  • Stochastic Processes
  • Theorems
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.