Geodesic
Numerical solution to stochastic differential equations on supercomputers
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 5-17.

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

This paper deals with some issues of the dependence of the accuracy of algorithms for the numerical solutions of stochastic differential equations (SDEs) on the size of an ensemble of simulated trajectories. The problems of accuracy arise due to the necessity of estimating functionals of SDEs-solutions with an increasing dispersion, a strong asymmetry of solutions distributions, indeterminacy of the time of arrival of trajectories of solutions at the boundaries of given domains. The ways of parallelization of statistical algorithms on a multi-processor cluster are described. The results of numerical experiments obtained on the supercomputer of Siberian Supercomputer Center are presented. 
@article{SJVM_2011_14_1_a1,
     author = {S. S. Artemiev and V. D. Korneev},
     title = {Numerical solution to stochastic differential equations on supercomputers},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a1/}
}
TY  - JOUR
AU  - S. S. Artemiev
AU  - V. D. Korneev
TI  - Numerical solution to stochastic differential equations on supercomputers
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2011
SP  - 5
EP  - 17
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a1/
LA  - ru
ID  - SJVM_2011_14_1_a1
ER  - 
%0 Journal Article
%A S. S. Artemiev
%A V. D. Korneev
%T Numerical solution to stochastic differential equations on supercomputers
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2011
%P 5-17
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a1/
%G ru
%F SJVM_2011_14_1_a1
S. S. Artemiev; V. D. Korneev. Numerical solution to stochastic differential equations on supercomputers. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a1/

[1] Artemev S. S., Chislennoe reshenie zadachi Koshi dlya sistem obyknovennykh i stokhasticheskikh differentsialnykh uravnenii, Izd-vo VTs SO RAN, Novosibirsk, 1993

[2] Averina T. A., Artemev S. S., “Chislennoe reshenie stokhasticheskikh differentsialnykh uravnenii s rastuschei dispersiei”, Sib. zhurn. vychisl. matematiki, 8:1 (2005), 1–10 | Zbl

[3] Averina T. A., Artemev S. S., “Analiz tochnosti metodov Monte-Karlo pri reshenii kraevykh zadach posredstvom veroyatnostnogo predstavleniya”, Sib. zhurn. vychisl. matematiki, 11:3 (2008), 239–250 | Zbl

[4] Ermakov S. M., Nekrutkin V. V., Sipin A. S., Sluchainye protsessy dlya resheniya klassicheskikh uravnenii matematicheskoi fiziki, Nauka, M., 1984 | MR | Zbl

[5] Korneev V. D., Parallelnoe programmirovanie v MPI, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2003

[6] Korneev V. D., Parallelnoe programmirovanie klasterov, Uchebn. posobie, Izd-vo NGTU, Novosibirsk, 2008

[7] Snir M., Otto S. W., Huss-Lederman S., Walker D., Dongarra J., MPI: The Complete Reference, MIT Press, Boston, 1996

[8] http://software.intel.com/ru-ru/intel-mkl/