Subadditive ergodic theorems for random sets in infinite dimensions

Jennie C. Hansen, Paul Hulse

Research output: Contribution to journalArticle

Abstract

We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in finite dimensions or with additional hypotheses on the random sets. We also show how the techniques can be used to obtain the strong law of large numbers for pairwise independent random sets, as well as results in the weak topology. © 2000 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)409-416
Number of pages8
JournalStatistics and Probability Letters
Volume50
Issue number4
Publication statusPublished - 1 Dec 2000

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Ergodic Theorem
Infinite Dimensions
Random Sets
Weak Topology
Strong law of large numbers
Independent Set
Pairwise
Banach space
Subset
Family

Keywords

  • Random sets
  • Subadditive ergodic theorem

Cite this

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Subadditive ergodic theorems for random sets in infinite dimensions. / Hansen, Jennie C.; Hulse, Paul.

In: Statistics and Probability Letters, Vol. 50, No. 4, 01.12.2000, p. 409-416.

Research output: Contribution to journalArticle

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