Level crossings of a two-parameter random walk

We prove that the number Z(N) of level crossings of a two-parameter simple random walk in its first NxN steps is almost surely N3/2+o(1) as N-->[infinity]. The main ingredient is a strong approximation of Z(N) by the crossing local time of a Brownian sheet. Our result provides a useful algorithm for simulating the level sets of the Brownian sheet.

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Year of publication:	2005
Authors:	Khoshnevisan, Davar ; Révész, Pál ; Shi, Zhan
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 115.2005, 3, p. 359-380
Publisher:	Elsevier
Keywords:	Level crossing Local time Random walk Brownian sheet

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

Persistent link: https://www.econbiz.de/10008875355