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

P. J. Fitzsimmons·K. Yano
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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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P. J. Fitzsimmons, K. Yano. 2006-09-05. Time change approach to generalized excursion measures, and its application to limit theorems. https://arxiv.org/abs/math/0608530

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