Open Access
Translator Disclaimer
March 2007 Large deviations and laws of the iterated logarithm for the local times of additive stable processes
Xia Chen
Ann. Probab. 35(2): 602-648 (March 2007). DOI: 10.1214/009117906000000601

Abstract

We study the upper tail behaviors of the local times of the additive stable processes. Let X1(t), …, Xp(t) be independent, d-dimensional symmetric stable processes with stable index 0<α≤2 and consider the additive stable process (t1, …, tp)=X1(t1)+⋯+Xp(tp). Under the condition d<αp, we obtain a precise form of the large deviation principle for the local time

ηx([0, t]p)=0t0tδx(X1(s1)+⋯+Xp(sp)) ds1⋯ dsp

of the multiparameter process (t1, …, tp), and for its supremum norm sup x∈ℝdηx([0, t]p). Our results apply to the law of the iterated logarithm and our approach is based on Fourier analysis, moment computation and time exponentiation.

Citation

Download Citation

Xia Chen. "Large deviations and laws of the iterated logarithm for the local times of additive stable processes." Ann. Probab. 35 (2) 602 - 648, March 2007. https://doi.org/10.1214/009117906000000601

Information

Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1121.60025
MathSciNet: MR2308590
Digital Object Identifier: 10.1214/009117906000000601

Subjects:
Primary: 60F10 , 60F15 , 60G52 , 60J55

Keywords: Additive stable process , large deviations , Law of the iterated logarithm , Local time

Rights: Copyright © 2007 Institute of Mathematical Statistics

JOURNAL ARTICLE
47 PAGES


SHARE
Vol.35 • No. 2 • March 2007
Back to Top