CUED Publications database

The ODE Method and Spectral Theory of Markov Operators

Huang, J and Kontoyiannis, I and Meyn, SP (2002) The ODE Method and Spectral Theory of Markov Operators. Proceedings of Stochastic Theory and Control Workshop, Springer, New York, pp. 205-221, B. Pasik-Duncan (Editor), 2002, 280. pp. 205-221. ISSN 0170-8643 (Unpublished)

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Abstract

We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are obtained: 1. Stability of an associated ODE implies that the stochastic recursion is stable in a strong sense when a gain parameter is small. 2. The range of gain-values is quantified through a spectral analysis of an associated linear operator, providing a non-local theory. 3. A second-order analysis shows precisely how variability leads to sensitivity of the algorithm with respect to the gain parameter. All results are obtained within the natural operator-theoretic framework of geometrically ergodic Markov processes.

Item Type: Article
Uncontrolled Keywords: math.PR math.PR math.DS
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 18 Aug 2020 12:42
DOI: