### Abstract

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

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 38 |

Volume | 736 |

Publication status | Published - 1996 |

### Publication series

Name | FEW Research Memorandum |
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Volume | 736 |

### Fingerprint

### Keywords

- limit theorems

### Cite this

*Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes*. (FEW Research Memorandum; Vol. 736). Tilburg: Econometrics.

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*Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes*. FEW Research Memorandum, vol. 736, vol. 736, Econometrics, Tilburg.

**Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes.** / Nieuwenhuis, G.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes

AU - Nieuwenhuis, G.

N1 - Pagination: 38

PY - 1996

Y1 - 1996

N2 - In Palm theory it is very common to consider several distributions to describe the characteristics of the system.To study a stationary marked point process, the time-stationary distribution P and its event-stationary Palm distributions P 0 L with respect to sets L of marks can all be used as starting point.When P is used, a modi ed, event-stationary version Q 0 L of P 0 L is de ned as the limit of an obvious discrete-time Ces aro average.In a sense this modi ed Palm distribution is more natural than the ordinary one.When a Palm distribution P 0 L 0 is taken as starting point, we can approximate another modi ed, event-stationary version of P 0 L by considering discrete-time Ces aro averages and a modi ed, time-stationary version QL of P by considering continuous-time Ces aro averages.These and other limit results are corollaries of uniform limit theorems for Ces aro averaged functionals.In essence, this paper presents a profound study of the relationship between P; P 0 L ; P 0 L 0, and modi ed versions of them, and their connections with ergodicity conditions and long-run averages of Ces aro type.

AB - In Palm theory it is very common to consider several distributions to describe the characteristics of the system.To study a stationary marked point process, the time-stationary distribution P and its event-stationary Palm distributions P 0 L with respect to sets L of marks can all be used as starting point.When P is used, a modi ed, event-stationary version Q 0 L of P 0 L is de ned as the limit of an obvious discrete-time Ces aro average.In a sense this modi ed Palm distribution is more natural than the ordinary one.When a Palm distribution P 0 L 0 is taken as starting point, we can approximate another modi ed, event-stationary version of P 0 L by considering discrete-time Ces aro averages and a modi ed, time-stationary version QL of P by considering continuous-time Ces aro averages.These and other limit results are corollaries of uniform limit theorems for Ces aro averaged functionals.In essence, this paper presents a profound study of the relationship between P; P 0 L ; P 0 L 0, and modi ed versions of them, and their connections with ergodicity conditions and long-run averages of Ces aro type.

KW - limit theorems

M3 - Report

VL - 736

T3 - FEW Research Memorandum

BT - Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes

PB - Econometrics

CY - Tilburg

ER -