A note on the sharp Lp-convergence rate of upcrossings to the Brownian local time

In this note, we prove a sharp Lp-rate of convergence of the number of upcrossings to the local time of the Brownian motion. In particular, it provides novel p-variation estimates (2<p<∞) for the number of upcrossings of the Brownian motion. Our result complements the fundamental work of Khoshnevisan (1994) who obtains an almost sure exact rate of convergence in the sup norm.

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Year of publication:	2015
Authors:	Ohashi, Alberto ; Simas, Alexandre B.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 100.2015, C, p. 137-141
Publisher:	Elsevier
Subject:	Brownian motion \| Local-time \| Upcrossings

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011263177