Numerical Methods in the Weak Sense for Stochastic Differential Equations with Small Noise
We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hiεj(h is a time increment, ε is a small parameter). We derive various efficient weak schemes for systems w...
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| Veröffentlicht in: | SIAM journal on numerical analysis 1997-12, Vol.34 (6), p.2142-2167 |
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| container_title | SIAM journal on numerical analysis |
| container_volume | 34 |
| creator | Milstein, G. N. M. V. Tret'Yakov |
| description | We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hiεj(h is a time increment, ε is a small parameter). We derive various efficient weak schemes for systems with small noise and study the Talay-Tubaro expansion of their global error. An efficient approach to reducing the Monte-Carlo error is presented. Some of the proposed methods are tested by calculating the Lyapunov exponent of a linear system with small noise. |
| doi_str_mv | 10.1137/S0036142996278967 |
| format | Article |
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N. ; M. V. Tret'Yakov</creator><creatorcontrib>Milstein, G. N. ; M. V. Tret'Yakov</creatorcontrib><description>We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hiεj(h is a time increment, ε is a small parameter). We derive various efficient weak schemes for systems with small noise and study the Talay-Tubaro expansion of their global error. An efficient approach to reducing the Monte-Carlo error is presented. 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| ispartof | SIAM journal on numerical analysis, 1997-12, Vol.34 (6), p.2142-2167 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Approximation Coefficients Computer simulation Differential equations Differentials Error rates Estimation methods Human error Inequality Methods Noise Numerical analysis Numerical methods Random variables Runge Kutta method |
| title | Numerical Methods in the Weak Sense for Stochastic Differential Equations with Small Noise |
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