Stochastic Approximation with Correlated Data

Abstract

New almost sure convergence results are developed for a special form of the multidimensional Robbins-Monro (RM) stochastic approximation procedure. The special form treated can be viewed as a stochastic approximation to the solution w = w sub o epsilon Rp of the linear equations Rw = P, where R is a pxp positive definite symmetric matrix. This special form commonly arises in adaptive signal processing applications. Essentially, previous convergence results for the RM procedure contain a common 'conditional expectation condition' which is extremely difficult (if not impossible) to satisfy when the 'training data' is a correlated sequence. In contrast, the new convergence results incorporate moment conditions and covariance function decay rate conditions. The ease with which these results can be applied in many cases is illustrated.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1976
Accession Number
ADA024279

Entities

People

  • David C. Farden
  • Louis L. Louis L. Scharf

Organizations

  • Colorado State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Colorado
  • Contracts
  • Convergence
  • Covariance
  • Department Of Defense
  • Electrical Engineering
  • Engineering
  • Equations
  • Inequalities
  • Military Research
  • Multivariate Analysis
  • Notation
  • Numbers
  • Probability
  • Random Variables
  • Signal Processing

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Statistical inference.