- Volume 9, Number 1 (2003), 1-24.
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 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 $T$.
Bernoulli, Volume 9, Number 1 (2003), 1-24.
First available in Project Euclid: 6 November 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Pitman, Jim; Yor, Marc. Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches. Bernoulli 9 (2003), no. 1, 1--24. doi:10.3150/bj/1068129008. https://projecteuclid.org/euclid.bj/1068129008