Geodesic
Calculation of the moments of sums for the autoregression process with signum by management
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 4, pp. 441-456 
L. Ya. Saveliev. Calculation of the moments of sums for the autoregression process with signum by management. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 4, pp. 441-456. http://geodesic.mathdoc.fr/item/SJVM_2008_11_4_a8/
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     author = {L. Ya. Saveliev},
     title = {Calculation of the moments of sums for the autoregression process with signum by management},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {441--456},
     year = {2008},
     volume = {11},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2008_11_4_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An autoregression sequence with simple management is considered. There is a sign of the previous term used in the recurrent equation determining this sequence. Multiplying this sign transforms this equation to a nonlinear one and essentially complicates the process. Such a signature management seems to be expedient, when an increment of the initial process is adjusted. The distributions and the moments of some random variables concerned with this process are investigated. The autoregression processes and examples of their application are described in detail in the literature [1–4].

[1] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Tom 1, Mir, M., 1984 | MR

[2] Shiryaev A. N., Veroyatnost, Nauka, M., 1989 | MR

[3] Shiryaev A. N., Osnovy stokhasticheskoi finansovoi matematiki, Tom 1, 2, Fazis, M., 1998

[4] Gerber Kh., Matematika strakhovaniya zhizni, Mir, M., 1995

[5] Kramer G., Matematicheskie metody statistiki, Mir, M., 1975 | MR

[6] Yu. V. Prokhorov (ed.), Veroyatnost i matematicheskaya statistika. Entsiklopediya, BRE, M., 1999 | MR

[7] Gnedenko B. V., Kurs teorii veroyatnostei, Nauka, M., 1988 | MR

[8] Natanson I. P., Proizvodnye, integraly i ryady. Entsiklopediya elementarnoi matematiki, Kniga 3, Gostekhizdat, M., 1952