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

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


P. J. Fitzsimmons, K. Yano



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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August 22, 2006