Convergence of the sum of reciprocal renewal times

Charles M. Newman

doi:10.1016/0167-7152(90)90071-E

Convergence of the sum of reciprocal renewal times

Charles M. Newman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Necessary and sufficient conditions are given for the almost sure convergence or divergence of ∑^∞_n=1(T₁+ ⋯ + T_n)^-1, where T₁, T₂,... are i.i.d. and positive.

Original language	English (US)
Pages (from-to)	185-187
Number of pages	3
Journal	Statistics and Probability Letters
Volume	10
Issue number	3
DOIs	https://doi.org/10.1016/0167-7152(90)90071-E
State	Published - Aug 1990

Keywords

Renewal processes
almost sure convergence
return times

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/0167-7152(90)90071-E

Cite this

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title = "Convergence of the sum of reciprocal renewal times",

abstract = "Necessary and sufficient conditions are given for the almost sure convergence or divergence of ∑∞n=1(T1+ ⋯ + Tn)-1, where T1, T2,... are i.i.d. and positive.",

keywords = "Renewal processes, almost sure convergence, return times",

author = "Newman, {Charles M.}",

note = "Funding Information: Research supported in part by NSF Grants Mathematical Sciences, New York University, DMS-8514834 and DMS-8902156. New York, NY 10012, USA.",

year = "1990",

month = aug,

doi = "10.1016/0167-7152(90)90071-E",

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journal = "Statistics and Probability Letters",

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AU - Newman, Charles M.

N1 - Funding Information: Research supported in part by NSF Grants Mathematical Sciences, New York University, DMS-8514834 and DMS-8902156. New York, NY 10012, USA.

PY - 1990/8

Y1 - 1990/8

N2 - Necessary and sufficient conditions are given for the almost sure convergence or divergence of ∑∞n=1(T1+ ⋯ + Tn)-1, where T1, T2,... are i.i.d. and positive.

AB - Necessary and sufficient conditions are given for the almost sure convergence or divergence of ∑∞n=1(T1+ ⋯ + Tn)-1, where T1, T2,... are i.i.d. and positive.

KW - Renewal processes

KW - almost sure convergence

KW - return times

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

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ER -

Convergence of the sum of reciprocal renewal times

Abstract

Keywords

ASJC Scopus subject areas

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