A problem of Foldes and Puri on the Wiener process
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- by Z. Shi PDF
- Trans. Amer. Math. Soc. 348 (1996), 219-228 Request permission
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 $X(t)=\int _0^{\tau (t)} \mathbb {1}_{\{|W(u)| \le \alpha t\}}\,du$ as $t$ tends to infinity, i.e. they ask: how long does $W$ stay in a tube before âcrossing very muchâ a given level? In this note, both limsup and liminf laws of the iterated logarithm are provided for $X$.References
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Additional Information
- Z. Shi
- Email: shi@ccr.jussieu.fr
- Received by editor(s): December 7, 1994
- © Copyright 1996 American Mathematical Society
- 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