Bernoulli

Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards

Joshua B. Levy and Murad S. Taqqu

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Abstract

It is well known that fractional Brownian motion can be obtained as the limit of a superposition of renewal reward processes with inter-renewal times that have infinite variance (heavy tails with exponent α) and with rewards that have finite variance. We show here that if the rewards also have infinite variance (heavy tails with exponent β) then the limit Zβ is a β-stable self-similar process. If β≤α, then Zβ is the Lévy stable motion with independent increments; but if β> α, then Zβ is a stable process with dependent increments and self-similarity parameter H = (β- α+ 1)/β.

Article information

Source
Bernoulli, Volume 6, Number 1 (2000), 23-44.

Dates
First available in Project Euclid: 22 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1082665378

Mathematical Reviews number (MathSciNet)
MR2001f:60023

Zentralblatt MATH identifier
0954.60071

Keywords
computer networks infinite variance self-similar processes stable processes telecommunications

Citation

Levy, Joshua B.; Taqqu, Murad S. Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli 6 (2000), no. 1, 23--44. https://projecteuclid.org/euclid.bj/1082665378


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References

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