On one technique of random processes analysis in continuous media

I. E. Poloskov

Matematičeskoe modelirovanie, Tome 15 (2003) no. 4, pp. 85-100.

Résumé

A new technique of moment equations derivation is considered for analysis of random processes in nonlinear continuous systems. Some examples demonstrate this technique.

Bibliographie

[1] Svetlitskii V. A., Sluchainye kolebaniya mekhanicheskikh sistem, Mashinostroenie, M., 1991 | MR

[2] Svetlitskii V. A., Mekhanika sterzhnei, Uchebnik dlya VTUZov. Ch. 2. Dinamika, Vysshaya shkola, M., 1987

[3] Solnes J., Stochastic processes and random vibrations. Theory and practice, John Wiley and Sons, New York, 1997 | Zbl

[4] Bolotin V. V., Sluchainye kolebaniya uprugikh sistem, Nauka, M., 1979 | MR | Zbl

[5] Bolotin V. V., Metody teorii veroyatnostei i teorii nadezhnosti v raschetakh sooruzhenii, Stroiizdat, M., 1982

[6] Makarov B. P., Nelineinye zadachi statisticheskoi dinamiki mashin i priborov, Mashinostroenie, M., 1983

[7] Nikolaenko N. A., Ulyanov S. V., Statisticheskaya dinamika mashinostroitelnykh konstruktsii, Mashinostroenie, M., 1977

[8] Konenkov Yu. K., Davtyan M. D., Sluchainye mekhanicheskie protsessy v oborudovanii mashin, Mashinostroenie, M., 1988

[9] Makeev V. P., Grinenko N. I., Pavlyuk Yu. S., Statisticheskie zadachi dinamiki uprugikh konstruktsii, Nauka, M., 1984

[10] Palmov V. A., Kolebaniya uprugo-plasticheskikh tel, Nauka, M., 1976

[11] Landa P. S., Avtokolebaniya v raspredelennykh sistemakh, Nauka, M., 1983 | MR | Zbl

[12] Kafarov V. V., Dorokhov I. N., Lipatov L. N., Sistemnyi analiz protsessov khimicheskoi tekhnologii, Nauka, M., 1982

[13] Klyatskin V. I., Stokhasticheskie uraneniya i volny v sluchaino neodnorodnykh sredakh, Nauka, M., 1980 | MR | Zbl

[14] Isimaru A., Rasprostranenie i rasseyanie voln v sluchaino-neodnorodnykh sredakh, t. 1, Mir, M., 1980; т. 2, 1981

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

[16] Rytov S. M., Kravtsov Yu. A., Tatarskii V. I., Vvedenie v statisticheskuyu radiofiziku, Ch. II, Nauka, M., 1978

[17] Vishik M. I., Fursikov A. V., Matematicheskie zadachi statisticheskoi gidromekhaniki, Nauka, M., 1980 | MR

[18] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, Ch. 2, M., 1967

[19] Sirazetdinov T. K., Optimizatsiya sistem s raspredelennymi parametrami, Nauka, M., 1977 | MR

[20] Sirazetdinov T. K., Ustoichivost sistem s raspredelennymi parametrami, Nauka, Novosibirsk, 1987 | MR | Zbl

[21] Potapov V. D., Stability of stochastic elastic and viscoelastic systems, John Wiley and Sons, New York, 1999 | Zbl

[22] Goncharenko V. M., “O sluchainykh kolebaniyakh uprugikh tel i teoriya markovskikh protsessov”, PM, 27:8 (1991), 95–100 | MR | Zbl

[23] Gardiner K. V., Stokhasticheskie zadachi v estestvennykh naukakh, Mir, M., 1986 | MR | Zbl

[24] Khaken G., Sinergetika, Mir, M., 1980 | MR

[25] Poloskov I. E., O svyazi momentov i kumulyantov mnogomernykh raspredelenii, Dep. v VINITI, No 8871-V86, Permskii un-t, Perm, 1986

[26] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR

[27] Christov C. I., “A complete orthogonal system of functions in $L^2(-\infty,\infty)$ space”, SIAM J. of Appl. Math., 42:6 (1982), 1337–1344 | DOI | MR | Zbl

[28] Wolfram S., The Mathematica Book, 3rd ed., University Press, Cambridge, 1996 | MR

[29] Heck A., Introduction to Maple, Springer-Verlag, Berlin, 1993 | MR | Zbl

[30] Avellaneda M. E. W., “Statistical properties of shocks in Burgers turbulence”, Communications in Math. Physics, 172:1 (1995), 13–38 | DOI | MR | Zbl

[31] Bkhatnagar P., Nelineinye volny v odnomernykh dispersnykh sistemakh, Mir, M., 1983 | MR | Zbl

[32] Katz A., Schuss Z., “Reliability of elastic structures driven by random loads”, SIAM J. Appl. Math., 45:3 (1985), 383–402 | DOI | MR | Zbl