A law of the iterated logarithm for stable processes in random scenery
The goal of this article is to present deterministically normalized laws of the iterated logarithm for stable processes in random scenery and random walks in random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence. To overcome some difficulties, the authors introduce and study quasi-associated collections of random variables, which may be of independent interest and worthy of further examination. Another source of interest in stable processes in random scenery is motivated by some newly found connections between this process and iterated Brownian motion [the authors, ``Stochastic calculus for Brownian motion on a Brownian fracture'' (Preprint, 1966)].
scientific article; zbMATH DE number 1364459
scientific article