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Factorial moment expansion for stochastic systems

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  • 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
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    References listed on IDEAS

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    1. Last, Günter, 1990. "Some remarks on conditional distributions for point processes," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 121-135, February.
    2. 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.
    3. Martin I. Reiman & Burton Simon, 1989. "Open Queueing Systems in Light Traffic," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 26-59, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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