Brownian intersection local times: Exponential moments and law of large masses
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- by Wolfgang König and Peter Mörters PDF
- Trans. Amer. Math. Soc. 358 (2006), 1223-1255 Request permission
Abstract:
Consider $p$ independent Brownian motions in $\mathbb {R}^d$, each running up to its first exit time from an open domain $B$, and their intersection local time $\ell$ as a measure on $B$. We give a sharp criterion for the finiteness of exponential moments, \[ \mathbb {E}\Big [\exp \Big (\sum _{i=1}^n \langle \varphi _i, \ell \rangle ^{1/p}\Big ) \Big ],\] where $\varphi _1, \dots , \varphi _n$ 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.References
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Additional Information
- Wolfgang König
- Affiliation: Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
- Address at time of publication: Mathematical Institute, University Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany
- Email: koenig@math.tu-berlin.de, koenig@math.uni-leipzig.de
- Peter Mörters
- Affiliation: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
- Email: maspm@bath.ac.uk
- Received by editor(s): August 13, 2003
- Received by editor(s) in revised form: May 4, 2004
- Published electronically: May 9, 2005
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 1223-1255
- MSC (2000): Primary 60J65, 60J55, 60F10
- DOI: https://doi.org/10.1090/S0002-9947-05-03744-X
- MathSciNet review: 2187652