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Tightness of pairs of tight càdlàg processes

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  • Schiopu-Kratina, Ioana

Abstract

A general theorem on necessary and sufficient conditions for the tightness of a sequence of càdlàg processes is given. This theorem is then used to derive necessary and sufficient conditions for the tightness in D([0, [infinity]), E1 x E2) of a sequence of pairs of càdlàg processes, which are individually tight in D([0, [infinity]), Ei), i = 1, 2. Both theorems are applied to point processes. As a consequence, it is proved that, if a sequence {Nn} of point processes and their compensators {An} are individually tight in D([0, [infinity]), R), then the sequence (Nn, An) is tight in D([0, [infinity]), R2).

Suggested Citation

  • Schiopu-Kratina, Ioana, 1985. "Tightness of pairs of tight càdlàg processes," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 167-177, December.
    • Handle: RePEc:eee:spapps:v:21:y:1985:i:1:p:167-177
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