Time Change Approach to Generalized Excursion Measures, and Its Application to Limit Theorems

Patrick J. Fitzsimmons and Kouji Yano ()
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Patrick J. Fitzsimmons: University of California
Kouji Yano: Osaka University

Journal of Theoretical Probability, 2008, vol. 21, issue 1, 246-265

Abstract: Abstract It is proved that generalized excursion measures can be constructed via time change of Itô’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.

Keywords: Itô’s excursion measure; Random time change; Conditional limit theorems; Bessel meander (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0108-8

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