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On renewal processes having stable inter-renewal intervals
and stable rewards
Joshua B. Levy
Murad S. Taqqu
Mandelbrot, and later Taqqu and Levy, have studied stationary
renewal reward processes that converge to self-similar processes.
The model is generalized here. The rewards are now in the domain of
attraction of a stable distribution with index ,
and the inter-renewal times are in the domain of attraction of a
stable distribution of index . The paper studies
the role that and play in the characterization
of the limit.