• 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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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.

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

First available in Project Euclid: 8 April 2004

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mixed moving average self-similarity stable distributions


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.

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