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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AMS subject classification (2000)
65C30, 65L06, 60H35, 60H10
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Rößler, A. Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise. Bit Numer Math 46, 97–110 (2006). https://doi.org/10.1007/s10543-005-0039-7
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DOI: https://doi.org/10.1007/s10543-005-0039-7