Geodesic
New frequency characteristics of the numerical solution to stochastic differential equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 1, pp. 15-26.

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The problems of the numerical analysis of stochastic differential equations with oscillatory solutions trajectories are studied. For the analysis of the numerical solution it is proposed to use the frequency response of generalizing the integral curve and the phase portrait. The results of numerical experiments carried out on a cluster of NCC-30T Siberian Supercomputer Center at the ICM SB RAS using a set of programs PARMONC are presented. 
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S. S. Artemiev; A. A. Ivanov; D. D. Smirnov. New frequency characteristics of the numerical solution to stochastic differential equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 1, pp. 15-26. http://geodesic.mathdoc.fr/item/SJVM_2015_18_1_a1/

[1] Dimentberg M. F., Nelineinye stokhasticheskie zadachi mekhanicheskikh kolebanii, Nauka, M., 1980 | MR

[2] Babitskii V. I., Teoriya vibroudarnykh sistem, Nauka, M., 1978 | MR

[3] Bykov V. V., Tsifrovoe modelirovanie v statisticheskoi radiotekhnike, Sovetskoe radio, M., 1971

[4] Palmov V. A., Teoriya uprugo-plasticheskikh tel, Nauka, M., 1976

[5] Rytov S. M., Vvedenie v statisticheskuyu radiofiziku, Nauka, M., 1966

[6] Neimark Yu. I., Landa P. S., Stokhasticheskie i khaoticheskie kolebaniya, Nauka, M., 1987 | MR

[7] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[8] Vallander S. V., Lektsii po gidroaerodinamike, Izd-vo LGU, L., 1978

[9] Artemev S. S., Yakunin M. A., Matematicheskoe i statisticheskoe modelirovanie v finansakh, Izd-vo IVMiMG SO RAN, Novosibirsk, 2008

[10] Marchenko M. A., Mikhailov G. A., “Raspredelënnye vychisleniya po metodu Monte-Karlo”, Avtomatika i telemekhanika, 2007, no. 5, 157–170 | MR | Zbl

[11] Artemev S. S., Chislennye metody resheniya zadachi Koshi dlya sistem obyknovennykh i stokhasticheskikh differentsialnykh uravnenii, Izd-vo VTs SO RAN, Novosibirsk, 1993

[12] Artemev S. S., Ivanov A. A., Korneev V. D., “Chislennyi analiz stokhasticheskikh ostsillyatorov na superkompyuterakh”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 15:1 (2012), 31–43 | Zbl