Escape Rates for Multidimensional Shift Self-similar Additive Sequences

First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on R d 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 seque...

Full description

Saved in:
Bibliographic Details
Published inJournal of theoretical probability Vol. 29; no. 3; pp. 896 - 921
Main Author Watanabe, Toshiro
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2016
Springer Nature B.V
Subjects
Brownian motion
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Self-similarity
Statistics
Stationary sequence of OU type
60G10
60G18
Shift self-similar additive sequence
Decomposable distribution
60G50
Online AccessGet full text

Cover

More Information
Summary:First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on R d 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 Lévy processes on R d and independent Brownian motions are given.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-015-0599-7