an:01529276
Zbl 0963.60032
Pipiras, Vladas; Taqqu, Murad S.
The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion
EN
Bernoulli 6, No. 4, 607-614 (2000).
00066608
2000
j
60G18 60K05
stable distributions; self-similar processes; renewal reward processes; stationary increments
There are considered a renewal reward process with both inter-renewal times and rewards that have heavy tails of exponents \(\alpha\) and \(\beta\), respectively, where \(1< \alpha< 2\), \(0<\beta<2\). It was proved by \textit{J. B. Levy} and \textit{M. S. Taqqu} [ibid. 6, No. 1, 23-44 (2000; Zbl 0954.60071)] that the suitably normalized renewal reward process converges to L??vy stable motion with index \(\beta\), possesses stationary increments and is self-similar in the case \(\beta>\alpha\). The limit process was identified through its finite-dimensional characteristic functions. The authors provide an integral representation for the process and show that it does not belong to the family of linear fractional stable motions.
Valentin Topchii (Omsk)
Zbl 0954.60071