An elementary renewal theorem for random compact convex sets
A set-valued analog of the elementary renewal theorem for Minkowski sums of random closed sets is considered. The corresponding renewal function is defined as where are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of H ( tK )/ t as t tends...
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| Veröffentlicht in: | Advances in applied probability 1995-12, Vol.27 (4), p.931-942 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A set-valued analog of the elementary renewal theorem for Minkowski sums of random closed sets is considered. The corresponding renewal function is defined as
where
are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of
H
(
tK
)/
t
as
t
tends to infinity. For
K
containing the origin as an interior point,
where
h
K
(
u
) is the support function of
K
and
is the set of all unit vectors
u
with
Eh
A
(
u
) > 0. Other set-valued generalizations of the renewal function are also suggested. |
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| ISSN: | 0001-8678 1475-6064 |
| DOI: | 10.1017/S0001867800047741 |