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
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
