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.
Citation
Vladas Pipiras. Murad S. Taqqu. "The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion." Bernoulli 6 (4) 607 - 614, August 2000.
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