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Coupling with compensators

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  • Last, Günter

Abstract

We propose two general methods for coupling marked point processes (MPPs) on the real half-line that are explicitly formulated in terms of (canonical) compensators. These couplings are related to several results in the literature as compensator bounds for the total variation distance between two MPPs and strong coupling of renewal processes. The coupling of two MPPs with different initial conditions but the same compensators will lead to finite coupling times if the compensator admits certain properties of regeneration or contractivity.

Suggested Citation

  • Last, Günter, 1996. "Coupling with compensators," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 147-170, December.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:2:p:147-170
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    References listed on IDEAS

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    1. Lindvall, Torgny, 1986. "On coupling of renewal processes with use of failure rates," Stochastic Processes and their Applications, Elsevier, vol. 22(1), pages 1-15, May.
    2. Thorisson, Hermann, 1995. "On time- and cycle-stationarity," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 183-209, February.
    3. Lindvall, Torgny, 1988. "Ergodicity and inequalities in a class of point processes," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 121-131, November.
    4. Last, Günter, 1993. "On dependent marking and thinning of point processes," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 73-94, March.
    5. Rolski, T. & Szekli, R., 1991. "Stochastic ordering and thinning of point processes," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 299-312, April.
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    Cited by:

    1. Last, Günter & Szekli, Ryszard, 1999. "Time and Palm stationarity of repairable systems," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 17-43, January.

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