Geodesic
On the asymptotics of the mean sojourn time of a~random walk on a~semi-axis
Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 449-466

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We find asymptotic expansions for the expectation of the sojourn time above an increasing level of a trajectory of a random walk with zero drift. The Cramér condition on the existence of an exponential moment is imposed on the distribution of jumps of the random walk.
Keywords: random walk, sojourn time, asymptotic analysis. 
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     title = {On the asymptotics of the mean sojourn time of a~random walk on a~semi-axis},
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V. I. Lotov; A. S. Tarasenko. On the asymptotics of the mean sojourn time of a~random walk on a~semi-axis. Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 449-466. http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a1/