Time change approach to generalized excursion measures, and its application to limit theorems
arXiv:math/0608530
Abstract
It is proved that generalized excursion measures can be constructed via time change of Ito's Brownian excursion measure. A tightness-like condition on strings is introduced to prove a convergence theorem of generalized excursion measures. The convergence theorem is applied to obtain a conditional limit theorem, a kind of invariance principle where the limit is the Bessel meander.
20 pages. Dedicated to Professor M. Fukushima on the occasion of his 70th birthday