Limit theorems for stochastic approximation algorithms

2011/02/23 by Henrik Renlund, Renlund, Henrik · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Markov Chains and Monte Carlo Methods #Simulation Techniques and Applications #Stochastic processes and financial applications #math.PR #msc:60G99 #msc:62L20

paper · pdf · doi:10.48550/arxiv.1102.4741

arxiv created 2011/02/23 · arxiv updated 2011/02/24

Abstract

We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these algorithms that in particular covers a generalized Pólya urn model, which is also discussed. In addition, we show how to scale these algorithms in some cases where we cannot determine the limiting distribution but expect it to be non-normal.

Citations

• A Stochastic Approximation Method
• Stochastic Estimation of the Maximum of a Regression Function

Cited by

• Stochastic approximation with random step sizes and urn models with random replacement matrices having finite mean

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