### 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 language | English |
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Pages (from-to) | 409-416 |

Number of pages | 8 |

Journal | Statistics and Probability Letters |

Volume | 50 |

Issue number | 4 |

Publication status | Published - 1 Dec 2000 |

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### Keywords

- Random sets
- Subadditive ergodic theorem

### Cite this

*Statistics and Probability Letters*,

*50*(4), 409-416.

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*Statistics and Probability Letters*, vol. 50, no. 4, pp. 409-416.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Subadditive ergodic theorems for random sets in infinite dimensions

AU - Hansen, Jennie C.

AU - Hulse, Paul

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

KW - Random sets

KW - Subadditive ergodic theorem

UR - http://www.scopus.com/inward/record.url?scp=0042208851&partnerID=8YFLogxK

M3 - Article

VL - 50

SP - 409

EP - 416

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -