Geodesic
Digital simulation of evolutionary stochastic differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1170-1179 
Yu. G. Bulychev; S. A. Pogonyshev. Digital simulation of evolutionary stochastic differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1170-1179. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a4/
@article{ZVMMF_1990_30_8_a4,
     author = {Yu. G. Bulychev and S. A. Pogonyshev},
     title = {Digital simulation of evolutionary stochastic differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1170--1179},
     year = {1990},
     volume = {30},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a4/}
}
TY  - JOUR
AU  - Yu. G. Bulychev
AU  - S. A. Pogonyshev
TI  - Digital simulation of evolutionary stochastic differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 1170
EP  - 1179
VL  - 30
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a4/
LA  - ru
ID  - ZVMMF_1990_30_8_a4
ER  - 
%0 Journal Article
%A Yu. G. Bulychev
%A S. A. Pogonyshev
%T Digital simulation of evolutionary stochastic differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 1170-1179
%V 30
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a4/
%G ru
%F ZVMMF_1990_30_8_a4

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

Euler, Euler–Cauchy, and Runge–Kutta difference schemes and fast Fourier transform procedures are used to develop efficient methods for the digital simulation of evolutionary stochastic partial differential equations that ensure the desired computational accuracy at minimum cost. Bounds of the computation errors are given.

[1] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[2] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[3] Ivanov V. V., Metody vychislenii na EVM, Nauk. dumka, Kiev, 1986 | MR

[4] Bulychev Yu. G., “Metod opornykh integralnykh krivykh resheniya zadachi Koshi dlya obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 28:10 (1988), 1482–1490 | MR

[5] Bulychev Yu. G., “Metod priblizhennogo resheniya dvukhmernogo uravneniya Fokkera–Planka”, Radiotekhn. i elektronika, 30:4 (1985), 727–730 | MR

[6] Bulychev Yu. G., Pogonyshev S. A., “Chislennyi metod analiza nelineinykh stokhasticheskikh sistem s ispolzovaniem algoritmov bystrogo preobrazovaniya Fure”, Izv. vuzov. Radioelektronika, 31:12 (1988), 12–17 | MR

[7] Bulychev Yu. G., Pogonyshev S. A., “Metod chislennogo integrirovaniya mnogomernogo uravneniya Fokkera–Planka na osnove usechennykh algoritmov bystrogo preobrazovaniya Fure”, Radiotekhn. i elektronika, 29:6 (1989), 1241–1249

[8] Nikitin N. N., Pervachev S. V., Razevig V. D., “Chislennoe reshenie stokhasticheskikh differentsialnykh uravnenii sledyaschikh sistem”, Avtomatika i telemekhan., 1975, no. 4, 133–137 | MR | Zbl

[9] Nikitin N. N., Razevig V. D., “Metody tsifrovogo modelirovaniya stokhasticheskikh differentsialnykh uravnenii i otsenka ikh pogreshnostei”, Zh. vychisl. matem. i matem. fiz., 18:1 (1978), 106–117 | MR | Zbl

[10] Rozovskii B. L., Evolyutsionnye stokhasticheskie sistemy, Nauka, M., 1983 | MR

[11] Milstein G. N., “Approximate integration of stochastic differential equations”, Theor. Probl. Appl., 19:3 (1974), 583–588 | MR

[12] Tikhonov V. I., Kulman N. K., Nelineinaya filtratsiya i kvazikogerentnyi priem signalov, Sov. radio, M., 1975

[13] Zadiraka V. K., “Otsenka preobrazovaniya Fure”, Kibernetika, 1971, no. 4, 58–63 | Zbl

[14] Stratonovich R. L., Uslovnye markovskie protsessy i ikh primenenie k teorii optimalnogo upravleniya, Izd-vo MGU, M., 1966 | MR

[15] Borovkov A. A., Matematicheskaya statistika, Nauka, M., 1984 | MR