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XV: 13, 191-205, LNM 850 (1981)
On Lévy's downcrossing theorem and various extensions (Excursion theory)
Lévy's downcrossing theorem describes the local time $L_t$ of Brownian motion at $0$ as the limit of $\epsilon D_t(\epsilon)$, where $D_t$ denotes the number of downcrossings of the interval $(0,\epsilon)$ up to time $t$. To give a simple proof of this result from excursion theory, easy to generalize, the paper uses the weaker definition of regenerative systems described in 1137. A gap in the related author's paper Zeit. für W-Theorie, 52, 1980 is repaired at the end of the paper
Keywords: Excursions, Lévy's downcrossing theorem, Local times, Regenerative systems
Nature: Original
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