On renewal processes having stable inter-renewal intervals and stable rewards

Joshua B. Levy
Murad S. Taqqu

Abstract:

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.