On the probability that integrated random walks stay positive

Vladislav Vysotsky

Stochastic Processes and their Applications, 2010, vol. 120, issue 7, 1178-1193

Abstract: Let Sn be a centered random walk with a finite variance, and consider the sequence , which we call an integrated random walk. We are interested in the asymptotics of as N-->[infinity]. Sinai (1992) [15] proved that pN[asymptotically equal to]N-1/4 if Sn is a simple random walk. We show that pN[asymptotically equal to]N-1/4 for some other kinds of random walks that include double-sided exponential and double-sided geometric walks, both not necessarily symmetric. We also prove that pN 0) is an exponential distribution.

Keywords: Integrated; random; walk; Area; of; random; walk; Unilateral; small; deviations; One-sided; exit; probability; Excursion; Area; of; excursion (search for similar items in EconPapers)
Date: 2010
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