Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches
Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches
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 …