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

2006/08/22 by P. J. Fitzsimmons, Fitzsimmons, P. J., K. Yano +1
Mathematics · #60F17 #60J25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60J25

paper · pdf · doi:10.48550/arxiv.math/0608530

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

arxiv created 2006/09/05 · arxiv updated 2009/12/01

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.

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