Equivalent necessary and sufficient conditions on noise sequences for stochastic approximation algorithms

I. Jeng Wang, Edwin K.P. Chong, Sanjeev R. Kulkarni

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We consider stochastic approximation algorithms on a general Hilbert space, and study four conditions on noise sequences for their analysis: Kushner and Clark's condition, Chen's condition, a decomposition condition, and Kulkarni and Horn's condition. We discuss various properties of these conditions. In our main result we show that the four conditions are all equivalent, and are both necessary and sufficient for convergence of stochastic approximation algorithms under appropriate assumptions.

Original languageEnglish (US)
Pages (from-to)784-801
Number of pages18
JournalAdvances in Applied Probability
Volume28
Issue number3
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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