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.

On different topologies for set-indexing collections / G. Aletti. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 54:1(2001), pp. 67-73.

On different topologies for set-indexing collections

G. Aletti
Primo
2001

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.
06a05; 60g40; Birth-and-growth processes; Primary: 60g05; Secondary: 60g07; Set-indexed processes; Topological space
Settore MAT/06 - Probabilita' e Statistica Matematica
2001
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/4827
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