Corpus ID: 210932380

# Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations

@article{Kuznetsov2020FourNF,
title={Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations},
author={D. Kuznetsov},
journal={arXiv: Probability},
year={2020}
}
The problem of the Taylor-Ito and Taylor-Stratonovich expansions of the Ito stochastic processes in a neighborhood of a fixed moment of time is considered. The classical forms of the Taylor-Ito and Taylor-Stratonovich expansions are transformed to the four new representations, which includes the minimal sets of different types of iterated Ito and Stratonovich stochastic integrals. Therefore, these representations (the so-called unified Taylor-Ito and Taylor-Stratonovich expansions) are more… Expand
8 Citations

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