### Resumé

Originalsprog | Engelsk |
---|---|

Tidsskrift | Journal of Applied Probability |

Vol/bind | 55 |

Udgave nummer | 3 |

Sider (fra-til) | 789-809 |

Antal sider | 21 |

ISSN | 0021-9002 |

DOI | |

Status | Udgivet - 1 sep. 2018 |

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

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

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

AU - Møller, Jesper

AU - Christoffersen, Andreas Dyreborg

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

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.

KW - Coupling

KW - Equilibrium

KW - Independent clustering

KW - Markov chain

KW - Pair correlation function

KW - Reproducing population weighted determinantal and permanental point processes

UR - http://www.scopus.com/inward/record.url?scp=85056790423&partnerID=8YFLogxK

U2 - 10.1017/jpr.2018.50

DO - 10.1017/jpr.2018.50

M3 - Journal article

VL - 55

SP - 789

EP - 809

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 3

ER -