On functionals of excursions for Bessel processes with negative index
Volume 246 / 2019
Studia Mathematica 246 (2019), 217-231
MSC: 60J25, 60J35, 60J45.
DOI: 10.4064/sm170309-15-3
Published online: 8 October 2018
Abstract
A closed formula is given for the integral of functionals on the space of excursions from a point $z\geq 0$ of a Bessel process $R^{(\mu )}$ with index $\mu \in (-1,0)$ with respect to the characteristic (Itô) measure. This integral is an integral with respect to some kernel $K$. The kernel $K$ is found due to the explicit form of the joint distribution of $(\tau _z, R_t^{(\mu )})$ at fixed time $t$ and for $\tau _z$ being the first hitting time of the point $z$ by the process $R^{(\mu )}$. The expected time spent by an excursion in an interval with respect to the Itô measure is calculated.
