Averaging Methods for the Asymptotic Analysis of Learning and Adaptive Systems, with Small Adjustment Rate.

Abstract

Recently proved theorems concerning weak convergence of non-Markovian processes to diffusions, together with an averaging and a stability method, are applied to two (learning or adaptive) processes of current interest: an automata model for route selection in telephone traffic routing, and an adaptive quantizer for use in transmission of random signals in communication theory. The models are chosen because they are prototypes of a large class to which the methods can be applied. The technique of application of the basic theorems to such processes is developed. Suitably interpolated and normalized 'learning or adaptive' processes converge weakly to a diffusion, as the 'learning or adaptation' rate goes to zero. For small learning rate, the qualitative properties (e.g., asymptotic (large-time) variances and parametric dependence) of the processes can be determined from the properties of the limit. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1980
Accession Number
ADA088110

Entities

People

  • Hai Huang
  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Automata
  • Convergence
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Engineering
  • Equations
  • Ergodic Processes
  • Learning
  • Mathematics
  • Models
  • Probability
  • Random Variables
  • Theorems
  • Weak Convergence

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  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.