Geodesic
Inequalities for the average exit time of a random walk from an~interval
Izvestiya. Mathematics , Tome 85 (2021) no. 4, pp. 745-754.

Voir la notice de l'article provenant de la source Math-Net.Ru

Two-sided inequalities are obtained for the average exit time from an interval for a random walk with zero and negative drift.
Keywords: boundary value problem, exit time from an interval, random walk, Wald's sequential criterion. 
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V. I. Lotov. Inequalities for the average exit time of a random walk from an~interval. Izvestiya. Mathematics , Tome 85 (2021) no. 4, pp. 745-754. http://geodesic.mathdoc.fr/item/IM2_2021_85_4_a5/

[1] A. Wald, Sequential analysis, John Wiley Sons, Inc., New York; Chapman Hall, Ltd., London, 1947, xii+212 pp. | MR | MR | Zbl | Zbl

[2] A. A. Borovkov, Probability theory, Universitext, Springer, London, 2013, xxviii+733 pp. | DOI | MR | Zbl

[3] A. Wald, J. Wolfowitz, “Optimum character of the sequential probability ratio test”, Ann. Math. Statist., 19:3 (1948), 326–339 | DOI | MR | Zbl

[4] D. Siegmund, Sequential analysis. Tests and confidence intervals, Springer Ser. Statist., Springer-Verlag, New York, 1985, xi+272 pp. | DOI | MR | Zbl

[5] V. I. Lotov, “Approximation of the expectation of the first exit time from an interval for a random walk”, Siberian Math. J., 57:1 (2016), 86–92 | DOI | DOI | MR | Zbl

[6] V. I. Lotov, “Asymptotic expansions in a sequential likelihood ratio test”, Theory Probab. Appl., 32:1 (1987), 57–67 | DOI | MR | Zbl

[7] A. N. Shiryaev, Optimal stopping rules, Appl. Math., 8, Springer-Verlag, New York–Heidelberg, 1978, x+217 pp. | MR | MR | Zbl | Zbl

[8] A. Gut, Stopped random walks. Limit theorems and applications, Springer Ser. Oper. Res. Financ. Eng., 2nd ed., Springer, New York, 2009, xiv+263 pp. | DOI | MR | Zbl

[9] A. A. Mogul'skii, “Absolute estimates for moments of certain boundary functionals”, Theory Probab. Appl., 18:2 (1973), 340–347 | DOI | MR | Zbl

[10] V. I. Lotov, “Bounds for the probability to leave the interval”, Statist. Probab. Lett., 145 (2019), 141–146 | DOI | MR | Zbl

[11] V. I. Lotov, “O nekotorykh neravenstvakh v granichnykh zadachakh dlya sluchainykh bluzhdanii”, Sib. elektron. matem. izv., 17 (2020), 661–671 | DOI | Zbl

[12] G. Lorden, “On excess over the boundary”, Ann. Math. Statist., 41:2 (1970), 520–527 | DOI | MR | Zbl

[13] A. A. Borovkov, Stochastic processes in queueing theory, Appl. Math., 4, Springer-Verlag, New York–Berlin, 1976, xi+280 pp. | DOI | MR | MR | Zbl | Zbl