@article{VNGU_2016_16_4_a6,
author = {V. I. Lotov and A. P. Lvov},
title = {Inequalities for the number of crossings of a strip by a random walk paths},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {65--71},
year = {2016},
volume = {16},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a6/}
}
TY - JOUR AU - V. I. Lotov AU - A. P. Lvov TI - Inequalities for the number of crossings of a strip by a random walk paths JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2016 SP - 65 EP - 71 VL - 16 IS - 4 UR - http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a6/ LA - ru ID - VNGU_2016_16_4_a6 ER -
V. I. Lotov; A. P. Lvov. Inequalities for the number of crossings of a strip by a random walk paths. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 4, pp. 65-71. http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a6/
[1] V. I. Lotov, N. G. Orlova, “On the number of crossings of a strip by sample paths of a random walk”, Sbornik: Mathematics, 194:6 (2003), 927–939 | DOI | DOI
[2] I. S. Borisov, “A note on the distribution of the number of crossings of a strip by a random walk”, Theory of Probability Its Applications, 53:2 (2009), 312–316 | DOI | DOI
[3] V. I. Lotov, “On an approach in two-sided boundary crossing problems”, Statistika i Upravlenie Sluchainymi Processami, Nauka, M., 1989, 117–121 (in Russian)
[4] V. I. Lotov, V. R. Khodjibayev, “On the number of crossings of a strip for stochastic processes with independent increments”, Siberian Advances in Mathematics, 3:2 (1993), 145–152
[5] V. I. Lotov, “On the limit behavior of the distribution of the crossing number of a strip by sample paths of a random walk”, Sib. Math. J., 54:2 (2013), 265–270 | DOI
[6] V. I. Lotov, N. G. Orlova, “Asymptotic expansions for the distribution of the crossing number of a strip by sample paths of a random walk”, Sib. Math. J., 45:4 (2004), 680–698 | DOI
[7] V. I. Lotov, “On the asymptotics of the ruin probability”, Theory of Probability Its Applications, 59:1 (2015), 154–163 | DOI | DOI
[8] Lorden G., “On the Excess over the Boundary”, Ann. Math. Stat., 41 (1970), 520–527 | DOI
[9] A. A. Borovkov, Probability Theory, Springer-Verlag, London, 2013
[10] Hajek B., “A Maximal Inequality for Supermartingales”, Electronic Communications in Probability, 19:55 (2014), 1–10
[11] Kugler J., Wachtel V., “Upper Bounds for the Maximum of a Random Walk with Negative Drift”, J. Appl. Probab., 50:4 (2013), 1131–1146 | DOI