Hitting, Occupation, and Inverse Local times of One-dimensional Diiusions: Martingale and Excursion Approaches

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