2020/03/28 by Dmitriy F. Kuznetsov, Mikhail D. Kuznetsov, Kuznetsov, Dmitriy F. +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.2003.14184
1598 pp., 20 Chapters, some typos were corrected
openalex publication_date 2020/03/28 · openalex created_date 2025/10/10 · arxiv created 2026/07/28 · openalex updated_date 2026/07/28 · arxiv updated 2026/07/30
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, 1246 pp., arXiv:2003.14184v76. Thus, both monographs are placed within a single submission, and their Internet links will differ only by the version numbers within arXiv:2003.14184.