Tightness of pairs of tight càdlàg processes

Ioana Schiopu-Kratina

Stochastic Processes and their Applications, 1985, vol. 21, issue 1, 167-177

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).

Keywords: Skorohod; tightness; stopping; times; point; processes; compensators (search for similar items in EconPapers)
Date: 1985
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