February 2024 On bivariate distributions of the local time of Itô-McKean diffusions
Jacek Jakubowski, Maciej Wiśniewolski
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Bernoulli 30(1): 227-251 (February 2024). DOI: 10.3150/23-BEJ1595

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 Lt in terms of convolution exponent and, using the excursion theory, we describe the transition density of the pair (X,L). 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 (Xt,L) 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

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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

Information

Received: 1 August 2022; Published: February 2024
First available in Project Euclid: 8 November 2023

MathSciNet: MR4665576
zbMATH: 07788882
Digital Object Identifier: 10.3150/23-BEJ1595

Keywords: Convolution Algebra , Excursion theory , Itô-McKean diffusion , Local time

Vol.30 • No. 1 • February 2024
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