The central limit problem for, infinite products of, and Lévy processes of renewal sequences

Bert Fristedt

doi:10.1007/BF00534944

The central limit problem for, infinite products of, and Lévy processes of renewal sequences

Bert Fristedt

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

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Abstract

Necessary and sufficient conditions are obtained for: (i) convergence of row products from a null triangular array of renewal sequences to a particular renewal sequence and (ii) convergence of an infinite product of renewal sequences to a non-trivial limit. These products correspond to intersections of regenerative phenomena of integers. Lévy processes of such regenerative phenomena are constructed.

Original language	English (US)
Pages (from-to)	479-507
Number of pages	29
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/BF00534944
State	Published - Dec 1981
Externally published	Yes

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10.1007/BF00534944

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title = "The central limit problem for, infinite products of, and L{\'e}vy processes of renewal sequences",

abstract = "Necessary and sufficient conditions are obtained for: (i) convergence of row products from a null triangular array of renewal sequences to a particular renewal sequence and (ii) convergence of an infinite product of renewal sequences to a non-trivial limit. These products correspond to intersections of regenerative phenomena of integers. L{\'e}vy processes of such regenerative phenomena are constructed.",

author = "Bert Fristedt",

year = "1981",

month = dec,

doi = "10.1007/BF00534944",

language = "English (US)",

volume = "58",

pages = "479--507",

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T1 - The central limit problem for, infinite products of, and Lévy processes of renewal sequences

AU - Fristedt, Bert

PY - 1981/12

Y1 - 1981/12

N2 - Necessary and sufficient conditions are obtained for: (i) convergence of row products from a null triangular array of renewal sequences to a particular renewal sequence and (ii) convergence of an infinite product of renewal sequences to a non-trivial limit. These products correspond to intersections of regenerative phenomena of integers. Lévy processes of such regenerative phenomena are constructed.

AB - Necessary and sufficient conditions are obtained for: (i) convergence of row products from a null triangular array of renewal sequences to a particular renewal sequence and (ii) convergence of an infinite product of renewal sequences to a non-trivial limit. These products correspond to intersections of regenerative phenomena of integers. Lévy processes of such regenerative phenomena are constructed.

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U2 - 10.1007/BF00534944

DO - 10.1007/BF00534944

M3 - Article

AN - SCOPUS:34250235749

SN - 0044-3719

VL - 58

SP - 479

EP - 507

JO - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

JF - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

IS - 4

ER -

The central limit problem for, infinite products of, and Lévy processes of renewal sequences

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