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On different topologies for set-indexing collections

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  • Aletti, Giacomo

Abstract

We underline some topological properties of set-indexing collections in order to provide new assumptions for set-indexed stochastic processes. We show that any of these topological assumptions is equivalent to another one already used in the framework of a set-indexed process. These may replace usual metric assumptions needed to derive some known stopping results. We provide an example related to a class of birth-and-growth processes.

Suggested Citation

  • Aletti, Giacomo, 2001. "On different topologies for set-indexing collections," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 67-73, August.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:1:p:67-73
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    Cited by:

    1. Aletti, Giacomo & Merzbach, Ely, 2002. "The set-indexed bandit problem," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 127-142, September.

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