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Stochastic recursive inclusions with non-additive iterate-dependent Markov noise

Yaji, Vinayaka G and Bhatnagar, Shalabh (2018) Stochastic recursive inclusions with non-additive iterate-dependent Markov noise. In: STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 90 (3). pp. 330-363.

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Official URL: http://dx.doi.org/10.1080/17442508.2017.1353984

Abstract

In this paper we study the asymptotic behaviour of stochastic approximation schemes with set-valued drift function and non-additive iterate-dependent Markov noise. We show that a linearly interpolated trajectory of such a recursion is an asymptotic pseudotrajectory for the flow of a limiting differential inclusion obtained by averaging the set-valued drift function of the recursion w.r.t. the stationary distributions of the Markov noise. The limit set theorem by Benaim is then used to characterize the limit sets of the recursion in terms of the dynamics of the limiting differential inclusion. We then state two variants of the Markov noise assumption under which the analysis of the recursion is similar to the one presented in this paper. Scenarios where our recursion naturally appears are presented as applications. These include controlled stochastic approximation, subgradient descent, approximate drift problem and analysis of discontinuous dynamics all in the presence of non-additive iterate-dependent Markov noise.

Item Type: Journal Article
Additional Information: Copy right for the article belong toTAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Department/Centre: Division of Interdisciplinary Research > Supercomputer Education & Research Centre
Depositing User: Id for Latest eprints
Date Deposited: 03 Apr 2018 18:26
Last Modified: 03 Apr 2018 18:26
URI: http://eprints.iisc.ac.in/id/eprint/59469

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