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Probability metrics and recursive algorithms

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

S. T. Rachev  and
L. Rüschendorf
S. T. Rachev*
Affiliation:
University of California at Santa Barbara
L. Rüschendorf*
Affiliation:
University of Freiburg
*
* Postal address: University of California, Statistics Department, Santa Barbara, CA 93106–3110, USA.
** Postal address: Universität Freiburg, Institüt Mathematische Stochastik, Hebelstr. 27, 79104 Freiburg, Germany.
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Abstract

It is shown by means of several examples that probability metrics are a useful tool to study the asymptotic behaviour of (stochastic) recursive algorithms. The basic idea of this approach is to find a ‘suitable' probability metric which yields contraction properties of the transformations describing the limits of the algorithm. In order to demonstrate the wide range of applicability of this contraction method we investigate examples from various fields, some of which have already been analysed in the literature.

Keywords

SEARCH ALGORITHMTRIECONTRACTION PROPERTIESPROBABILITY METRICSIMAGE ENCODING

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 770 - 799
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by a DFG Grant and NATO Grant CRG 900798.

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