From infinite urn schemes to self-similar stable processes
Durieu, Olivier; Samorodnitsky, Gennady; Wang, Yizao
We investigate the randomized Karlin model with parameter beta in (0,1), which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fractional Brownian motion with Hurst index beta/2 in (0,1/2). We show here that when the randomization is heavy-tailed with index alpha in (0,2), then the odd-occupancy process scales to a (beta/alpha)-self-similar symmetric alpha-stable process with stationary increments.
inifinite urn scheme; regular variation; stable process; self-similar process; functional central limit theorem