A problem of Földes
and Puri on the Wiener process
Author:
Z. Shi
Journal:
Trans. Amer. Math. Soc. 348 (1996), 219-228
MSC (1991):
Primary 60J65; Secondary 60G17
DOI:
https://doi.org/10.1090/S0002-9947-96-01485-7
MathSciNet review:
1321589
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a real-valued Wiener process starting from 0, and
be the right-continuous inverse process of its local time at 0. Földes and Puri [3] raise the problem of studying the almost sure asymptotic behavior of
as
tends to infinity, i.e. they ask: how long does
stay in a tube before ``crossing very much" a given level? In this note, both limsup and liminf laws of the iterated logarithm are provided for
.
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- 3 A. Földes and M.L. Puri, The time spent by the Wiener process in a narrow tube before leaving a wide tube, Proc. Amer. Math. Soc. 117 (1993), 529--536, MR 93d:60131.
- 4 J.W. Pitman and M. Yor, A decomposition of Bessel bridges, Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 (1982), 425--457, MR 84a:60091.
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Additional Information
Z. Shi
Email:
shi@ccr.jussieu.fr
DOI:
https://doi.org/10.1090/S0002-9947-96-01485-7
Keywords:
Wiener process (Brownian motion),
law of the iterated logarithm
Received by editor(s):
December 7, 1994
Article copyright:
© Copyright 1996
American Mathematical Society