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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, USA

    Patrick J. Fitzsimmons

  2. Department of Mathematics, Osaka University, Osaka, Japan

    Kouji Yano

Authors
  1. Patrick J. Fitzsimmons
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  2. Kouji Yano
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Correspondence to Kouji Yano.

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Dedicated to Professor Masatoshi Fukushima on the occasion of his seventieth birthday.

K. Yano is supported by JSPS Research Fellowships for Young Scientists.

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Fitzsimmons, P.J., Yano, K. Time Change Approach to Generalized Excursion Measures, and Its Application to Limit Theorems. J Theor Probab 21, 246–265 (2008). https://doi.org/10.1007/s10959-007-0108-8

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  • DOI: https://doi.org/10.1007/s10959-007-0108-8

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