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. AlettiPrimo
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.File in questo prodotto:
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