Large deviations for renormalized self-intersection local times of stable processes

Abstract

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β\in (2d/3,d]. We find a difference between the upper and lower tail. In addition, we find that the behavior of the lower tail depends critically on whether β<d or β=d.

Published at http://dx.doi.org/10.1214/009117904000001099 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
• Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks

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