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Brownian intersection local times: Exponential moments and law of large masses

Wolfgang Koenig·Peter Moerters
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Abstract

Consider p independent Brownian motions in R^d, each running up to its first exit time from an open domain B, and their intersection local time l as a measure on B. We give a sharp criterion for the finiteness of exponential moments, E[exp(\sum_{i=1}^n (int_B f_i(x) l(dx))^{1/p})], where f_1, ...,f_n are nonnegative, bounded functions with compact support in B. We also derive a law of large numbers for intersection local time conditioned to have large total mass.

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Wolfgang Koenig, Peter Moerters. 2003-08-15. Brownian intersection local times: Exponential moments and law of large masses. https://arxiv.org/abs/math/0308150

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