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Maxima of moving sums in a Poisson random field

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Hock Peng Chan
Hock Peng Chan*
Affiliation:
National University of Singapore
*
∗ Postal address: Department of Statistics and Applied Probability, Faculty of Science, National University of Singapore, Science Drive 1, 119260, Singapore. Email address: stachp@nus.edu.sg
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Abstract

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In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

Keywords

Change of measureGaussian processlarge deviationsmarked Poisson processmoving sumsrandom fieldscan statistics

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G10: Stationary processes 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 3 , September 2009 , pp. 647 - 663
Copyright
Copyright © Applied Probability Trust 2009 

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