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Article

Török, Csaba
A note on the Runge-Kutta method for stochastic differential equations. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 1, pp. 121-124
MSC: 60H10, 65L05 | MR 1173753 | Zbl 0753.60052
Keywords:
stochastic differential equation; Runge--Kutta method; monotonicity and Lipschitz condition
Summary:
In the paper the convergence of a mixed Runge--Kutta method of the first and second orders to a strong solution of the Ito stochastic differential equation is studied under a monotonicity condition.
References:
[1] Rümelin W.: Numerical treatment of stochastic differential equations. SIAM J. Numer. Anal. 19 (1982), 604-613. MR 0656474
[2] Aljushina L.A.: Lomanyje Eulera dlja uravnenij Ito s monotonnymi koefficientami. Teor. Veroyatnost. i Primenen. 33 (1987), 367-373.
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