Displaying similar documents to “Global stochastic approximation”

On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

Peggy Cénac (2013)

ESAIM: Probability and Statistics

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We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as...

Asymptotic normality of randomly truncated stochastic algorithms

Jérôme Lelong (2013)

ESAIM: Probability and Statistics

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We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function,...

Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda (2018)

Applications of Mathematics

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We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different...