Stochastic Approximation with Discontinuous Dynamics and State Dependent Noise: w.p.1 Convergence.

Abstract

Stochastic approximations might not be continuous and the noise sequence (xi sub n) might depend on (X sub n). An 'averaging' and an 'ordinary differential equation' method are combined to get w.p.1 convergence for both the above algorithm and for the case where the iterates are projected back onto a bounded set G if they ever leave it. Two examples are developed, the first being an automata problem where the dynamics are not smooth and the noise is state dependent, and the second a Robbins-Monro process with observation averaging (which causes the noise to be state dependent). Each example is typical of a larger class.

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Document Details

Document Type
Technical Report
Publication Date
Jul 10, 1980
Accession Number
ADA089777

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Automata
  • Convergence
  • Dynamics
  • Equations
  • Intervals
  • Linear Systems
  • Markov Processes
  • Mathematics
  • Numbers
  • Observation
  • Probability
  • Random Variables
  • Sequences
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

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