Excursion measure away from an exit boundary of one-dimensional diffusion processes (Q863795)

A measure generalizing the excursion measure away from an exit boundary is constructed for a one-dimensional diffusion process via the desintegration formula with respect to the lifetime. It is used to generalize the convergence theorem of \textit{Y. Kasahara} and \textit{S. Watanabe} [Ill. J. Math. 50, No. 1--4, 515--539 (2006; Zbl 1102.60066)] in terms of the Poisson point fields, where the inverse local time processes of regular diffusions converge in law to a Lévy process related to a diffusion with an exit boundary.