Local asymptotics of the cycle maximum of a heavy-tailed random walk
Local asymptotics of the cycle maximum of a heavy-tailed random walk
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Publisher
Cambridge, UK: Cambridge University Press
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Language
English
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Publisher
Cambridge, UK: Cambridge University Press
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Contents
Let ξ, ξ1, ξ2,… be a sequence of independent and identically distributed random variables, and let S
n
=ξ1+⋯+ξ
n
and M
n
=max
k≤n
S
k
. Let τ=min{n≥1: S
n
≤0}. We assume that ξ has a heavy-tailed distribution and negative, finite mean E(ξ)<0. We find the asymptotics of P{Mτ ∈ (x, x+T]} as x→∞, for a fixed, positi...
Alternative Titles
Full title
Local asymptotics of the cycle maximum of a heavy-tailed random walk
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Record Identifier
TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_aap_1175266476
Permalink
https://devfeature-collection.sl.nsw.gov.au/record/TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_aap_1175266476
Other Identifiers
ISSN
0001-8678
E-ISSN
1475-6064
DOI
10.1239/aap/1175266476
