Title: Hitting, occupation, and inverse local times of one-dimensional diffusions: martingale and excursion approaches
Author: Jim Pitman and Marc Yor
Date: November 2001
Abstract:
Basic relations between the distributions of hitting, occupation, 
and inverse local times of a one-dimensional diffusion process $X$, first 
discussed by \Ito-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 $T$.