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May 2021 Compound Poisson approximation for regularly varying fields with application to sequence alignment
Bojan Basrak, Hrvoje Planinić
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Bernoulli 27(2): 1371-1408 (May 2021). DOI: 10.3150/20-BEJ1278

Abstract

The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces which appears to be of independent interest. We further introduce a novel and convenient concept of anchoring of the extremal clusters for regularly varying sequences and fields. Together with the Poissonian approximation theory, this allows for a concise description of the limiting behavior of random fields in this setting. We apply this theory to shed entirely new light on the classical problem of evaluating local alignments of biological sequences.

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Bojan Basrak. Hrvoje Planinić. "Compound Poisson approximation for regularly varying fields with application to sequence alignment." Bernoulli 27 (2) 1371 - 1408, May 2021. https://doi.org/10.3150/20-BEJ1278

Information

Received: 1 November 2019; Revised: 1 September 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1278

Keywords: compound Poisson approximation , Gumbel distribution , local sequence alignment , point process , Random fields , regular variation , tail process

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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