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Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor-Stratonovich expansion. (English. Russian original) Zbl 1469.65032

Comput. Math. Math. Phys. 60, No. 3, 379-389 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 3, 379-390 (2020).
Summary: A strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor-Stratonovich expansion is proposed. The focus is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical simulation of which is the main difficulty in the implementation of the proposed numerical method.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

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