IJPAM: Volume 15, No. 4 (2004)

INCREMENTS OF THE PRINCIPAL VALUE
OF BROWNIAN MOTION LOCAL TIME

Abdelkader Bahram
Laboratoire de Mathématiques
Université Djillali Liabès
B.P. 89, 22000 Sidi Bel Abbès, ALGERIA
e-mail: Abdelkader_bahram@yahoo.fr


Abstract.Let $W$ be a standard Brownian motion and define $Y(t)=\int_{0}^{t}\frac{ds}{W(s)}$ as Cauchy's value related to local time. In this paper we prove
\begin{multline*} \hspace{-13pt}\lim_{T\longrightarrow\infty}\Sup_{0\leq t\leq T... ...og \log a_T\right)\right)^{\frac{1}{2}}}\\ =2,\quad \text{a.s.}, \end{multline*}
where $ 0\leq\alpha\leq 2$ under suitable conditions on $a_T$.

Received: June 3, 2004

AMS Subject Classification: 60J65

Key Words and Phrases: local time, large increment, Brownian motion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 4