%0 Journal Article %1 pitman2003hitting %A Pitman, Jim %A Yor, Marc %D 2003 %J Bernoulli %K diffusions excursions hitting_times laplace_transform local_times occupation_time review %N 1 %P 1-24 %R 10.3150/bj/1068129008 %T Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches. %V 9 %X Summary: Basic relations between the distributions of hitting, occupation and inverse local times of a one-dimensional diffusion process $X$, first discussed by K. Itô and H. P. McKean jun. ``Diffusion processes and their sample paths'' (1965; Zbl 0127.09503), are reviewed from the perspectives of martingale 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 $T$.

@article{pitman2003hitting, abstract = {{Summary: Basic relations between the distributions of hitting, occupation and inverse local times of a one-dimensional diffusion process $X$, first discussed by {\it K. It\^o} and {\it H. P. McKean jun.} [``Diffusion processes and their sample paths'' (1965; Zbl 0127.09503)], are reviewed from the perspectives of martingale 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 $T$.}}, added-at = {2010-08-26T20:57:36.000+0200}, author = {Pitman, Jim and Yor, Marc}, biburl = {https://www.bibsonomy.org/bibtex/2af18ef33b84971e852358ff3c9728f8d/peter.ralph}, classmath = {{*60J55 (Additive functionals) }}, doi = {10.3150/bj/1068129008}, interhash = {39ddb848ac7a374fa90954b46177cbd8}, intrahash = {af18ef33b84971e852358ff3c9728f8d}, journal = {Bernoulli }, keywords = {diffusions excursions hitting_times laplace_transform local_times occupation_time review}, language = {English}, number = 1, pages = {1-24}, timestamp = {2010-08-26T20:57:36.000+0200}, title = {Hitting, occupation and inverse local times of one-dimensional diffusions: {Martingale} and excursion approaches.}, volume = 9, year = 2003 }