Time change approach to generalized excursion measures, and its application to limit theorems

Details Time change approach to generalized excursion measures, and its application to limit theorems Time change approach to generalized excursion measures, and its application to limit theorems

2006-08-22

arxiv.org/abs/math/0608530v2

Mathematics

Probability

20 pages. Dedicated to Professor M. Fukushima on the occasion of his 70th birthday

Scientific paper

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.

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