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February 2003 Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches
Jim Pitman, Marc Yor
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Bernoulli 9(1): 1-24 (February 2003). DOI: 10.3150/bj/1068129008

Abstract

Basic relations between the distributions of hitting, occupation and inverse local times of a one-dimensional diffusion process $X$, first discussed by It\^o and McKean, are reviewed from the perspectives of martingale calculus and excursion theory. These relations, and the technique of conditioning on $L_T^y$, the local time of $X$ at level $y$ before a suitable random time $T$, yield formulae for the joint Laplace transform of $L_T^y$ and the times spent by $X$ above and below level $y$ up to time $T$.

Citation

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Jim Pitman. Marc Yor. "Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches." Bernoulli 9 (1) 1 - 24, February 2003. https://doi.org/10.3150/bj/1068129008

Information

Published: February 2003
First available in Project Euclid: 6 November 2003

zbMATH: 1024.60032
MathSciNet: MR1963670
Digital Object Identifier: 10.3150/bj/1068129008

Keywords: arcsine law , Feynman-Kac formula , last exit decomposition

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

Vol.9 • No. 1 • February 2003
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