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.
A hard copy of this manuscript is available from the
first-named author upon request.
The manuscript can be downloaded in
dvi form (74K)
and pdf form (177K).
(Version of September 5, 2006)
The manuscript is also available at arXiv.org--click here.
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August 22, 2006