Abstract
Denote as L the local time at 0 of an Itô-McKean diffusion X. We present a new explicit description of the distribution of in terms of convolution exponent and, using the excursion theory, we describe the transition density of the pair . We provide a simple connection formula for the distribution of excursions of a bivariate Itô-McKean diffusion from a hyperplane. Examples involving the distribution of a local time are presented, including a formula for the distribution of for a transient diffusion.
Acknowledgements
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Jacek Jakubowski. Maciej Wiśniewolski. "On bivariate distributions of the local time of Itô-McKean diffusions." Bernoulli 30 (1) 227 - 251, February 2024. https://doi.org/10.3150/23-BEJ1595
