Brownian intersection local times: Exponential moments and law of large masses |
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| Authors: | Wolfgang Kö nig Peter Mö rters |
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| Affiliation: | Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany ; Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom |
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| Abstract: | Consider  independent Brownian motions in  , each running up to its first exit time from an open domain  , and their intersection local time  as a measure on  . We give a sharp criterion for the finiteness of exponential moments,
where  are nonnegative, bounded functions with compact support in  . We also derive a law of large numbers for intersection local time conditioned to have large total mass. |
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| Keywords: | Intersection of Brownian paths intersection local time exponential moment Feynman-Kac formula |
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