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Journal of Theoretical Probability

, Volume 21, Issue 1, pp 246–265 | Cite as

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

  • Patrick J. Fitzsimmons
  • Kouji Yano
Article

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 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of MathematicsOsaka UniversityOsakaJapan

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