Level crossings of a two-parameter random walk

Davar Khoshnevisan, Pál Révész and Zhan Shi

Stochastic Processes and their Applications, 2005, vol. 115, issue 3, 359-380

Abstract: 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.

Keywords: Level; crossing; Local; time; Random; walk; Brownian; sheet (search for similar items in EconPapers)
Date: 2005
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