IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v56y1995i2p321-335.html
   My bibliography  Save this article

Factorial moment expansion for stochastic systems

Author

Listed:
  • Blaszczyszyn, B.

Abstract

For a given functional of a simple point process, we find an analogue of Taylor's theorem for its mean value. The terms of the expansion are integrals of some real functions with respect to factorial moment measures of the point process. The remainder term is an integral of some functional with respect to a higher order Campbell measure. A special case of this expansion is Palm-Khinchin formula. The results complement previous studies of Reiman and Simon (1989), Baccelli and Brémaud (1993) and shed new light on light traffic approximations of Daley and Rolski (1994), Blaszczyszyn and Rolski (1993).

Suggested Citation

  • Blaszczyszyn, B., 1995. "Factorial moment expansion for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 321-335, April.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:321-335
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00071-Z
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daley, D. J. & Rolski, T., 1994. "Light traffic approximations in general stationary single-server queues," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 141-158, January.
    2. Martin I. Reiman & Burton Simon, 1989. "Open Queueing Systems in Light Traffic," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 26-59, February.
    3. Last, Günter, 1990. "Some remarks on conditional distributions for point processes," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 121-135, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Blaszczyszyn, Bartlomiej & Merzbach, Ely & Schmidt, Volker, 1997. "A note on expansion for functionals of spatial marked point processes," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 299-306, December.
    2. Baccelli, François & Hasenfuss, Sven & Schmidt, Volker, 1999. "Differentiability of functionals of Poisson processes via coupling with applications to queueing theory," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 299-321, June.
    3. Ayhan, Hayriye & Schlegel, Sabine, 2001. "Expansion formulae for characteristics of cumulative cost in finite horizon production models," European Journal of Operational Research, Elsevier, vol. 132(1), pages 50-61, July.
    4. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Igor Kovalenko, 1997. "Ergodic and light traffic properties of a complex repairable system," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 387-409, October.
    2. Jean-François Coeurjolly & Jesper Møller & Rasmus Waagepetersen, 2017. "A Tutorial on Palm Distributions for Spatial Point Processes," International Statistical Review, International Statistical Institute, vol. 85(3), pages 404-420, December.
    3. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    4. Blaszczyszyn, Bartlomiej & Merzbach, Ely & Schmidt, Volker, 1997. "A note on expansion for functionals of spatial marked point processes," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 299-306, December.
    5. Cao, Xi-Ren, 1996. "Perturbation analysis of discrete event systems: Concepts, algorithms, and applications," European Journal of Operational Research, Elsevier, vol. 91(1), pages 1-13, May.
    6. Baccelli, François & Hasenfuss, Sven & Schmidt, Volker, 1999. "Differentiability of functionals of Poisson processes via coupling with applications to queueing theory," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 299-321, June.
    7. Ayhan, Hayriye & Schlegel, Sabine, 2001. "Expansion formulae for characteristics of cumulative cost in finite horizon production models," European Journal of Operational Research, Elsevier, vol. 132(1), pages 50-61, July.
    8. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:321-335. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.