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October 2004 Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
Richard F. Bass, Xia Chen
Ann. Probab. 32(4): 3221-3247 (October 2004). DOI: 10.1214/009117904000000504

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→∞.

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Richard F. Bass. Xia Chen. "Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm." Ann. Probab. 32 (4) 3221 - 3247, October 2004. https://doi.org/10.1214/009117904000000504

Information

Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1075.60097
MathSciNet: MR2094444
Digital Object Identifier: 10.1214/009117904000000504

Subjects:
Primary: 60J55
Secondary: 60F10 , 60J55

Keywords: Critical exponent , Gagliardo–Nirenberg inequality , Intersection local time , large deviations , Law of the iterated logarithm , Self-intersection local time

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 4 • October 2004
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