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Author Younes, Laurent
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Asymptotic Behaviour ♦ Markovian Stochastic Algorithm ♦ Exploding Regime ♦ Robbins-monro Type ♦ Natural Strategy ♦ Rapidly Decreasing Ergodicity Rate ♦ Markovian Noise ♦ Classic Robbins-monro Form ♦ Sure Convergence Cannot ♦ Control Parameter ♦ Positive Probability ♦ Diffusion Approximation Theorem ♦ Markov Chain ♦ Markovian Noise Form ♦ Stochastic Algorithm ♦ Introduction Stochastic Algorithm
Description . We analyse the convergence of stochastic algorithms with Markovian noise when the ergodicity of the Markov chain governing the noise rapidly decreases as the control parameter tends to infinity. In such a case, there may be a positive probability of divergence of the algorithm in the classic Robbins-Monro form. We provide modifications of the algorithm which ensure convergence. Moreover, we analyse the asymptotic behaviour of these algorithms and state a diffusion approximation theorem. 1. Introduction Stochastic algorithms of Robbins-Monro type with Markovian noise form a category of processes for which almost sure convergence cannot be obtained in general. The reason is that the ergodicity of the Markov chain governing the noise may decrease when the control parameter tends to infinity, and trap the algorithm within an exploding regime. In this paper, we study rigorously a natural strategy in which more time is spent for estimating the variations of the control parameter for large...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1998-01-01
Publisher Institution Stochastics and Stochastics Models