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An Iterative Monte Carlo Scheme for Generating Lie Group-Valued Random Variables

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  01 July 2016

Mauro Piccioni  and
Sergio Scarlatti
Mauro Piccioni*
Affiliation:
Università di L'Aquila
Sergio Scarlatti*
Affiliation:
Università di L'Aquila
*
* Postal address: Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, 67100 L'Aquila, Italy.
* Postal address: Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, 67100 L'Aquila, Italy.
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Abstract

In this paper a simple approximation scheme is proposed for the problem of generating and computing expectations of functionals of a wide class of random variables with values in a compact Lie group. The algorithm is suggested by the time-discretization of an ergodic diffusion leaving invariant the distribution of interest. It is shown to converge as the discretization step goes to zero with the iterations in a natural way.

Keywords

IMAGE PROCESSINGSPIN SYSTEMSERGODIC DIFFUSION

MSC classification

Primary: 82C80: Numerical methods (Monte Carlo, series resummation, etc.)
Secondary: 68U10: Image processing
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 616 - 628
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Supported by 40% MURST Processi Stocastici e Calcolo Stocastico.

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