Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
MathSciNet review: 1321589
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $W$ be a real-valued Wiener process starting from 0, and $\tau (t)$ 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 $X(t)=\int _0^{\tau (t)} {\text{\bf 1}\hskip -1.25pt\mathrm{l}}_{\{ | W(u)| \le \alpha t\} }du$ as $t$ tends to infinity, i.e. they ask: how long does $W$ 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 $X$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 60J65, 60G17

Retrieve articles in all journals with MSC (1991): 60J65, 60G17

Additional Information

Z. Shi

Keywords: Wiener process (Brownian motion), law of the iterated logarithm
Received by editor(s): December 7, 1994
Article copyright: © Copyright 1996 American Mathematical Society