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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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