Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise |
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Authors: | Andreas Rößler |
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Affiliation: | (1) Fachbereich Mathematik, Darmstadt University of Technology, Schlossgartenstr. 7, D-64289 Darmstadt, Germany |
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Abstract: | A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance. |
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Keywords: | stochastic Runge– Kutta method stochastic differential equation colored rooted tree analysis weak approximation numerical method |
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