Pair correlation functions and limiting distributions of iterated cluster point processes

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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Resumé

We consider a Markov chain of point processes such that each state is a superposition of an independent cluster process with the previous state as its centre process together with some independent noise process and a thinned version of the previous state. The model extends earlier work by Felsenstein (1975) and Shimatani (2010) describing a reproducing population. We discuss when closed-form expressions of the first- and second-order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument.
OriginalsprogEngelsk
TidsskriftJournal of Applied Probability
Vol/bind55
Udgave nummer3
Sider (fra-til)789-809
Antal sider21
ISSN0021-9002
DOI
StatusUdgivet - 1 sep. 2018

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Pair Correlation Function
Point Process
Limiting Distribution
Markov chain
Equilibrium Distribution
Superposition
Closed-form
Moment
First-order
Converge
Limiting distribution
Point process
Equilibrium distribution
Model

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    Pair correlation functions and limiting distributions of iterated cluster point processes. / Møller, Jesper; Christoffersen, Andreas Dyreborg.

    I: Journal of Applied Probability, Bind 55, Nr. 3, 01.09.2018, s. 789-809.

    Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

    TY - JOUR

    T1 - Pair correlation functions and limiting distributions of iterated cluster point processes

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    AB - We consider a Markov chain of point processes such that each state is a superposition of an independent cluster process with the previous state as its centre process together with some independent noise process and a thinned version of the previous state. The model extends earlier work by Felsenstein (1975) and Shimatani (2010) describing a reproducing population. We discuss when closed-form expressions of the first- and second-order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument.

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    KW - Equilibrium

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    JO - Journal of Applied Probability

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