Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes

    Research output: Book/ReportReportProfessional

    236 Downloads (Pure)

    Abstract

    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.
    Original languageEnglish
    Place of PublicationTilburg
    PublisherEconometrics
    Number of pages38
    Volume736
    Publication statusPublished - 1996

    Publication series

    NameFEW Research Memorandum
    Volume736

    Fingerprint

    Marked Point Process
    Palm Distribution
    Ergodicity
    Stationary Distribution
    Discrete-time
    Long-run
    Limit Theorems
    Continuous Time
    Corollary

    Keywords

    • limit theorems

    Cite this

    Nieuwenhuis, G. (1996). Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes. (FEW Research Memorandum; Vol. 736). Tilburg: Econometrics.
    Nieuwenhuis, G. / Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes. Tilburg : Econometrics, 1996. 38 p. (FEW Research Memorandum).
    @book{e9963ce3420e49b588cc95f908dbcb1d,
    title = "Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes",
    abstract = "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.",
    keywords = "limit theorems",
    author = "G. Nieuwenhuis",
    note = "Pagination: 38",
    year = "1996",
    language = "English",
    volume = "736",
    series = "FEW Research Memorandum",
    publisher = "Econometrics",

    }

    Nieuwenhuis, G 1996, 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.

    Tilburg : Econometrics, 1996. 38 p. (FEW Research Memorandum; Vol. 736).

    Research output: Book/ReportReportProfessional

    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 -

    Nieuwenhuis G. Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes. Tilburg: Econometrics, 1996. 38 p. (FEW Research Memorandum).