The Annals of Probability

Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm

Richard F. Bass and Xia Chen

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Abstract

If βt is renormalized self-intersection local time for planar Brownian motion, we characterize when $\mathbb{E}e^{\gamma\beta_{1}}$ is finite or infinite in terms of the best constant of a Gagliardo–Nirenberg inequality. We prove large deviation estimates for β1 and −β1. We establish lim sup  and lim inf  laws of the iterated logarithm for βt as t→∞.

Article information

Source
Ann. Probab., Volume 32, Number 4 (2004), 3221-3247.

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883352

Digital Object Identifier
doi:10.1214/009117904000000504

Mathematical Reviews number (MathSciNet)
MR2094444

Zentralblatt MATH identifier
1075.60097

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 60J55: Local time and additive functionals 60F10: Large deviations

Keywords
Intersection local time Gagliardo–Nirenberg inequality law of the iterated logarithm critical exponent self-intersection local time large deviations

Citation

Bass, Richard F.; Chen, Xia. Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm. Ann. Probab. 32 (2004), no. 4, 3221--3247. doi:10.1214/009117904000000504. https://projecteuclid.org/euclid.aop/1107883352


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