Bernoulli

  • Bernoulli
  • Volume 6, Number 4 (2000), 607-614.

The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion

Vladas Pipiras and Murad S. Taqqu

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Abstract

Levy and Taqqu (2000) considered a renewal reward process with both inter-renewal times and rewards that have heavy tails with exponents α and β, respectively. When 1<α<β< 2 and the renewal reward process is suitably normalized, the authors found that it converges to a symmetric β-stable process Zβ(t), t∈[0,1] which possesses stationary increments and is self-similar. They identified the limit process through its finite-dimensional characteristic functions. We provide an integral representation for the process and show that it does not belong to the family of linear fractional stable motions.

Article information

Source
Bernoulli, Volume 6, Number 4 (2000), 607-614.

Dates
First available in Project Euclid: 8 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081449595

Mathematical Reviews number (MathSciNet)
MR2001g:60111

Zentralblatt MATH identifier
0963.60032

Keywords
mixed moving average self-similarity stable distributions

Citation

Pipiras, Vladas; Taqqu, Murad S. The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli 6 (2000), no. 4, 607--614. https://projecteuclid.org/euclid.bj/1081449595


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References

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