Geodesic
Digital simulation of evolutionary stochastic differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1170-1179 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[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