### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 36 |

Volume | 2005-7 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2005-7 |

### Fingerprint

### Keywords

- point processes
- non-stationarity
- family of Palm distributions
- domination

### Cite this

*Dominated Families of Shifted Palm Distributions*. (CentER Discussion Paper; Vol. 2005-7). Tilburg: Econometrics.

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**Dominated Families of Shifted Palm Distributions.** / Nieuwenhuis, G.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Dominated Families of Shifted Palm Distributions

AU - Nieuwenhuis, G.

N1 - Pagination: 36

PY - 2005

Y1 - 2005

N2 - In stationary point process theory, the concept Palm distribution plays an important role.Many important results (like for instance Little s law, so important in many fields) arise from it.However, in the non-stationary case a whole family of local Palm distributions (PD s) has to be considered and the concept seems to loose its importance.The present paper mainly considers non-stationary point processes, and studies relations between the distribution P of a point process, the family {Px} of PD s, and the family {P0,x} of shifted PD s.Here P0,x is the probability distribution that is experienced from an occurrence (arrival, point, transaction) at x.It is attempted to regain some of the glance of the concept Palm distribution by considering generalizations of results that are basic for stationary point processes.Starting point is a refined version of Campbell s equation, which expresses the general relationship between the distribution P of the point process and the family {Px} of PD s.It is used to generalize the inversion formula, well known from stationary point process theory.This generalization is basic; it leads to several relations regarding the above distributions.In the second part of the research domination assumptions are imposed: either the null-sets of a time-stationary distribution are also null-sets of P or the nullsets of one event-stationary distribution are also null-sets of almost all shifted PD s.Under such domination regulations, P0,x can explicitly be expressed in terms of P and several stationary-case long-run properties can be generalized.The relationship between the two types of domination assumptions is carefully studied.

AB - In stationary point process theory, the concept Palm distribution plays an important role.Many important results (like for instance Little s law, so important in many fields) arise from it.However, in the non-stationary case a whole family of local Palm distributions (PD s) has to be considered and the concept seems to loose its importance.The present paper mainly considers non-stationary point processes, and studies relations between the distribution P of a point process, the family {Px} of PD s, and the family {P0,x} of shifted PD s.Here P0,x is the probability distribution that is experienced from an occurrence (arrival, point, transaction) at x.It is attempted to regain some of the glance of the concept Palm distribution by considering generalizations of results that are basic for stationary point processes.Starting point is a refined version of Campbell s equation, which expresses the general relationship between the distribution P of the point process and the family {Px} of PD s.It is used to generalize the inversion formula, well known from stationary point process theory.This generalization is basic; it leads to several relations regarding the above distributions.In the second part of the research domination assumptions are imposed: either the null-sets of a time-stationary distribution are also null-sets of P or the nullsets of one event-stationary distribution are also null-sets of almost all shifted PD s.Under such domination regulations, P0,x can explicitly be expressed in terms of P and several stationary-case long-run properties can be generalized.The relationship between the two types of domination assumptions is carefully studied.

KW - point processes

KW - non-stationarity

KW - family of Palm distributions

KW - domination

M3 - Discussion paper

VL - 2005-7

T3 - CentER Discussion Paper

BT - Dominated Families of Shifted Palm Distributions

PB - Econometrics

CY - Tilburg

ER -