Geodesic
Asymptotic expansions for the distribution of the sojourn time of a~random walk on a~half-axis
Informatics and Automation, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 154-164.

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

A complete asymptotic expansion for $n\to\infty$ is obtained in a local limit theorem for the distribution of the sojourn time of a random walk with zero drift in the set $(b,\infty)$ during $n$ steps. Here $b=b(n)\to\infty$, $b(n)=o(n)$, and Cramér-type conditions are imposed on the distribution of jumps of the walk. 
@article{TRSPY_2013_282_a12,
     author = {V. I. Lotov},
     title = {Asymptotic expansions for the distribution of the sojourn time of a~random walk on a~half-axis},
     journal = {Informatics and Automation},
     pages = {154--164},
     publisher = {mathdoc},
     volume = {282},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a12/}
}
TY  - JOUR
AU  - V. I. Lotov
TI  - Asymptotic expansions for the distribution of the sojourn time of a~random walk on a~half-axis
JO  - Informatics and Automation
PY  - 2013
SP  - 154
EP  - 164
VL  - 282
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a12/
LA  - ru
ID  - TRSPY_2013_282_a12
ER  - 
%0 Journal Article
%A V. I. Lotov
%T Asymptotic expansions for the distribution of the sojourn time of a~random walk on a~half-axis
%J Informatics and Automation
%D 2013
%P 154-164
%V 282
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a12/
%G ru
%F TRSPY_2013_282_a12
V. I. Lotov. Asymptotic expansions for the distribution of the sojourn time of a~random walk on a~half-axis. Informatics and Automation, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 154-164. http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a12/

[1] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 2, Mir, M., 1984

[2] Spitser F., Printsipy sluchainogo bluzhdaniya, Mir, M., 1969

[3] Skorokhod A.V., Slobodenyuk N.P., Predelnye teoremy dlya sluchainykh bluzhdanii, Nauk. dumka, Kiev, 1970 | MR | Zbl

[4] Borodin A.N., Ibragimov I.A., Predelnye teoremy dlya funktsionalov ot sluchainykh bluzhdanii, Tr. MIAN, 195, Nauka, SPb., 1994 | MR | Zbl

[5] Borovkov A.A., “Novye predelnye teoremy v granichnykh zadachakh dlya summ nezavisimykh slagaemykh”, Sib. mat. zhurn., 3:5 (1962), 645–694 | MR | Zbl

[6] Lotov V.I., “Predelnye teoremy v odnoi granichnoi zadache dlya sluchainykh bluzhdanii”, Sib. mat. zhurn., 40:5 (1999), 1095–1108 | MR | Zbl

[7] Lotov V.I., “Asimptoticheskii analiz raspredelenii v dvugranichnykh zadachakh. II”, Teoriya veroyatn. i ee primen., 24:4 (1979), 873–879 | MR | Zbl

[8] Semenov A.T., “Asimptoticheskie razlozheniya dlya raspredeleniya vremeni prebyvaniya sluchainogo bluzhdaniya v otrezke”, Sib. mat. zhurn., 15:4 (1974), 918–930 | Zbl

[9] Lugavov V.S., Rogozin B.A., “Faktorizatsionnye predstavleniya dlya vremen prebyvaniya polumarkovskikh bluzhdanii”, Sib. mat. zhurn., 42:2 (2001), 389–406 | MR | Zbl

[10] Lugavov V.S., “O komponentakh faktorizatsionnogo predstavleniya dlya vremeni prebyvaniya polunepreryvnykh sluchainykh bluzhdanii v polose”, Sib. mat. zhurn., 44:4 (2003), 800–809 | MR | Zbl

[11] Lotov V.I., “Faktorizatsionnye tozhdestva dlya vremeni prebyvaniya sluchainogo bluzhdaniya v polose”, Sib. mat. zhurn., 51:1 (2010), 146–155 | MR | Zbl

[12] Lotov V.I., “O vremeni prebyvaniya sluchainogo bluzhdaniya v polose”, Sib. mat. zhurn., 51:4 (2010), 785–804 | MR | Zbl

[13] Borovkov A.A., Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya, Nauka, M., 1972 | MR

[14] Khardi G.G., Raskhodyaschiesya ryady, Izd-vo inostr. lit., M., 1951

[15] Rogozin B.A., “Asimptotika koeffitsientov v teoremakh Levi–Vinera ob absolyutno skhodyaschikhsya trigonometricheskikh ryadakh”, Sib. mat. zhurn., 14:6 (1973), 1304–1312 | MR | Zbl

[16] De Brëin N.G., Asimptoticheskie metody v analize, Izd-vo inostr. lit., M., 1961