Escape Rates for Multidimensional Shift Self-similar Additive Sequences

摘要

First the relation between shift self-similar additive sequences and stationary sequences of Ornstein-Uhlenbeck type (OU type) on is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary sequences of OU type are solved. Some applications to laws of the iterated logarithm for strictly stable L,vy processes on and independent Brownian motions are given.