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arXiv · 2003.14184

Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB

Dmitriy F. Kuznetsov·Mikhail D. Kuznetsov
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Abstract

This monograph is devoted to the problem of numerical integration of stochastic differential equations (SDEs), mainly Ito SDEs. More precisely, the book mainly discusses high-order strong numerical methods with orders of accuracy 1.0, 1.5, 2.0, 2.5, and 3.0 for SDEs. The Euler (Euler-Maruyama) method for Ito SDEs is also considered. Moreover, weak numerical methods for Ito SDEs are presented. This book contains 20 chapters divided into 4 parts. This book has many overlaps with the monograph: Dmitriy F. Kuznetsov, Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs, 2026, 1248 pp., https://arxiv.org/abs/2003.14184v82. Thus, both monographs are placed within a single submission, and their Internet links will differ only by the version numbers within https://arxiv.org/abs/2003.14184

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Dmitriy F. Kuznetsov, Mikhail D. Kuznetsov. 2020-03-28. Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB. https://arxiv.org/abs/2003.14184

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