Time Change Approach to Generalized Excursion Measures, and Its Application to Limit Theorems |
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| Authors: | Patrick J. Fitzsimmons Kouji Yano |
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| Affiliation: | (1) Department of Mathematics, University of California, San Diego, USA;(2) Department of Mathematics, Osaka University, Osaka, Japan |
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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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| Keywords: | It?’ s excursion measure Random time change Conditional limit theorems Bessel meander |
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