Geodesic
Inequalities for the sojourn time of random walk above a certain boundary
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 434-451.

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Under general conditions, we obtain inequalities for moments of sojourn time of a random walk over linear boundary. We find asymptotics of these moments for random walks with regular or semi-exponential distribution of summands.
Keywords: random walk, sojourn time, inequalities. 
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A. S. Tarasenko. Inequalities for the sojourn time of random walk above a certain boundary. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 434-451. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a46/

[1] A. A. Borovkov, Probability Theory, Librokom, M., 2009

[2] A. A. Borovkov, K. A. Borovkov, Asymptotical analysis of random walks, v. 1, Slowly varying distributions of jumps, Fizmatlit, M., 2008, 652 pp.

[3] S. V. Nagaev, “Some Limit Theorems for Large Deviations”, Theory of Probability and its Applications, 10:2 (1965), 214–-235 | DOI | MR | Zbl

[4] Spitzer F., Principles of Random Walks, 2nd ed., Springer-Verlag, New York, 1976 | MR