Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111186
Title: Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noises
Authors: Milstein, G. N.
Tret'yakov, M. V.
Issue Date: 1997
Publisher: Society for Industrial and Applied Mathematics Publications
Society for Industrial & Applied Mathematics (SIAM)
Citation: Milstein G. N. Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noises / G. N. Milstein, M. V. Tret'yakov // SIAM Journal of Scientific Computing. — 1997. — Vol. 18. — Iss. 4. — P. 1067-1087.
Abstract: A new approach to the construction of mean-square numerical methods for the solution of stochastic differential equations with small noises is proposed. The approach is based on expanding the exact solution of the system with small noises in powers of time increment and small parameter. The theorem on the mean-square estimate of method errors is proved. Various efficient numerical schemes are derived for a general system with small noises and for systems with small additive and small colored noises. The proposed methods are tested by calculation of Lyapunov exponents and simulation of a laser Langevin equation with multiplicative noises.
Keywords: COMPUTER SIMULATION
SMALL NOISES
STOCHASTIC DIFFERENTIAL EQUATIONS
LASER LANGEVIN EQUATION
LYAPUNOV EXPONENTS
MEAN SQUARE NUMERICAL METHODS
STOCHASTIC DIFFERENTIAL EQUATIONS
COMPUTER SIMULATION
DIFFERENTIAL EQUATIONS
ERROR ANALYSIS
ESTIMATION
LYAPUNOV METHODS
RANDOM PROCESSES
THEOREM PROVING
NUMERICAL METHODS
URI: http://hdl.handle.net/10995/111186
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 0031173522
ISSN: 1064-8275
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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