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

Richard F. Bass·Xia Chen
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Abstract

If β_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{γβ_1} is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for β_1 and -β_1. We establish lim sup and lim inf laws of the iterated logarithm for β_t as t\to\infty.

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Richard F. Bass, Xia Chen. 2005-03-25. Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm. https://doi.org/10.1214/009117904000000504

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