Brownian intersection local times: Exponential moments and law of large masses
Abstract
Consider p independent Brownian motions in Rd, 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(Σi=1n (intB fi(x) l(dx))1/p)], where f1, ...,fn 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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