Long random walk excursions and local time

Miklós Csörgo and Pál Révész

Stochastic Processes and their Applications, 1992, vol. 41, issue 2, 181-190

Abstract: It is well known that the number of excursions of short, as well as long, duration of a Wiener process away from x that are completed by time t can be used to determine its local time process [eta](x,t). Let M(a,x,n) be the number of excursions of duration greater than a of a simple symmetric random walk Sk,k = 0, 1, ..., away from that are of duration greater than a in length and are completed by time n. We show here that if M (a,x,n) is suitably regulated by requiring that a = an be not too big, then it can also determine its local time process [xi](x,n) with appropriate rates of convergence.

Keywords: simple; symmetric; random; walk; long; excursions; local; time; Wiener; process; measure; du; voisinage (search for similar items in EconPapers)
Date: 1992
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