Geodesic
The asymptotic behavior of the mean sojourn time for a random walk to be above a receding curvilinear boundary
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 18-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the asymptotic behavior of the mean sojourn time for a random walk to be above a receding curved boundary in the case where the jump distribution satisfies the Cramer condition.
Keywords: random walk, mean sojourn time, large deviations. 
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I. S. Borisov; E. I. Shefer. The asymptotic behavior of the mean sojourn time for a random walk to be above a receding curvilinear boundary. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 18-27. http://geodesic.mathdoc.fr/item/VNGU_2017_17_4_a1/

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[2] V. I. Lotov, A. S. Tarasenko, “On the asymptotics of the mean sojourn time of a random walk on a semi-axis”, Izv. Math., 79:3 (2015), 449–466 | DOI | DOI | MR | Zbl | Zbl

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[4] A. A. Borovkov, Probability Theory, Librocom, M., 2009 (in Russian)