Probability theory and mathematical statistics

On the sojourn time of random walk above a certain boundary

A. S. Tarasenko

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: The asymptotics of the expected sojourn time of a random walk over linear and nonlinear boundaries is found. We assume that right tail distribution of random walk summands varies regularly. In the case of linear boundary the corresponding result is obtained for random walks with semi-exponential distribution of summands.

Keywords: random walk, sojourn time, asymptotic analysis.

UDC: 519.21

MSC: 60F10

Received November 20, 2014, published July 12, 2015

DOI: 10.17377/semi.2015.12.034