Small ball probabilities for a class of time-changed self-similar processes

This paper establishes small ball probabilities for a class of time-changed processes X∘E, where X is a self-similar process and E is an independent continuous process, each with a certain small ball probability. In particular, examples of the outer process X and the time change E include an iterated fractional Brownian motion and the inverse of a general subordinator with infinite Lévy measure, respectively. The small ball probabilities of such time-changed processes show power law decay, and the rate of decay does not depend on the small deviation order of the outer process X, but on the self-similarity index of X.