[2003.14184] Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2003.14184 (math) [Submitted on 28 Mar 2020 ( v1 ), last revised 31 Aug 2026 (this version, v83)] Title: Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB Authors: Dmitriy F. Kuznetsov , Mikhail D. Kuznetsov View a PDF of the paper titled Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB, by Dmitriy F. Kuznetsov and 1 other authors View PDF 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 Comments: 1599 pp. Some inaccuracies have been corrected Subjects: Probability (math.PR) Cite as: arXiv:2003.14184 [math.PR] (or arXiv:2003.14184v83 [math.PR] for this version) https://doi.org/10.48550/arXiv.2003.14184 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dmitriy Feliksovich Kuznetsov [ view email ] [v1] Sat, 28 Mar 2020 03:22:52 UTC (207 KB) [v2] Mon, 6 Apr 2020 07:22:06 UTC (211 KB) [v3] Tue, 21 Apr 2020 12:21:08 UTC (213 KB) [v4] Sun, 10 May 2020 11:15:00 UTC (215 KB) [v5] Sat, 30 May 2020 20:26:30 UTC (215 KB) [v6] Mon, 29 Jun 2020 15:59:52 UTC (215 KB) [v7] Sun, 19 Jul 2020 22:35:26 UTC (220 KB) [v8] Mon, 10 Aug 2020 12:24:33 UTC (219 KB) [v9] Tue, 1 Sep 2020 16:42:31 UTC (222 KB) [v10] Thu, 1 Oct 2020 09:19:34 UTC (224 KB) [v11] Sun, 1 Nov 2020 07:20:06 UTC (230 KB) [v12] Tue, 1 Dec 2020 05:07:35 UTC (231 KB) [v13] Mon, 4 Jan 2021 07:46:04 UTC (241 KB) [v14] Mon, 1 Feb 2021 06:59:57 UTC (246 KB) [v15] Mon, 12 Apr 2021 12:42:19 UTC (247 KB) [v16] Mon, 10 May 2021 05:49:31 UTC (254 KB) [v17] Tue, 1 Jun 2021 04:40:47 UTC (263 KB) [v18] Thu, 1 Jul 2021 04:08:13 UTC (273 KB) [v19] Mon, 2 Aug 2021 00:18:22 UTC (288 KB) [v20] Wed, 1 Sep 2021 06:15:39 UTC (292 KB) [v21] Sun, 3 Oct 2021 14:58:36 UTC (292 KB) [v22] Mon, 1 Nov 2021 04:13:12 UTC (293 KB) [v23] Wed, 1 Dec 2021 13:30:07 UTC (293 KB) [v24] Mon, 3 Jan 2022 09:14:29 UTC (302 KB) [v25] Tue, 1 Feb 2022 16:11:11 UTC (313 KB) [v26] Tue, 1 Mar 2022 05:18:12 UTC (317 KB) [v27] Sat, 2 Apr 2022 05:12:35 UTC (321 KB) [v28] Sun, 1 May 2022 17:51:35 UTC (321 KB) [v29] Wed, 1 Jun 2022 10:24:36 UTC (321 KB) [v30] Sun, 3 Jul 2022 06:39:11 UTC (324 KB) [v31] Mon, 1 Aug 2022 15:46:21 UTC (333 KB) [v32] Thu, 1 Sep 2022 16:09:02 UTC (336 KB) [v33] Sun, 2 Oct 2022 17:51:07 UTC (337 KB) [v34] Tue, 1 Nov 2022 04:20:04 UTC (338 KB) [v35] Mon, 12 Dec 2022 07:33:58 UTC (339 KB) [v36] Sun, 1 Jan 2023 22:13:09 UTC (343 KB) [v37] Wed, 1 Feb 2023 05:11:51 UTC (345 KB) [v38] Wed, 1 Mar 2023 07:28:13 UTC (345 KB) [v39] Mon, 3 Apr 2023 06:07:36 UTC (347 KB) [v40] Mon, 1 May 2023 04:04:02 UTC (347 KB) [v41] Thu, 1 Jun 2023 07:12:52 UTC (348 KB) [v42] Mon, 3 Jul 2023 11:20:13 UTC (354 KB) [v43] Tue, 1 Aug 2023 04:08:03 UTC (359 KB) [v44] Fri, 1 Sep 2023 06:07:40 UTC (359 KB) [v45] Sun, 1 Oct 2023 19:15:12 UTC (362 KB) [v46] Wed, 1 Nov 2023 06:17:23 UTC (363 KB) [v47] Fri, 1 Dec 2023 17:06:39 UTC (367 KB) [v48] Sun, 28 Jan 2024 17:06:36 UTC (368 KB) [v49] Sun, 11 Feb 2024 16:05:08 UTC (371 KB) [v50] Mon, 4 Mar 2024 03:13:01 UTC (382 KB) [v51] Mon, 1 Apr 2024 05:47:35 UTC (394 KB) [v52] Wed, 1 May 2024 04:17:32 UTC (402 KB) [v53] Sat, 1 Jun 2024 12:00:53 UTC (403 KB) [v54] Thu, 18 Jul 2024 02:59:57 UTC (407 KB) [v55] Fri, 2 Aug 2024 17:12:00 UTC (407 KB) [v56] Sun, 1 Sep 2024 14:05:43 UTC (407 KB) [v57] Sun, 13 Oct 2024 16:17:10 UTC (408 KB) [v58] Mon, 4 Nov 2024 14:04:33 UTC (410 KB) [v59] Sun, 1 Dec 2024 05:15:37 UTC (416 KB) [v60] Wed, 1 Jan 2025 08:57:54 UTC (417 KB) [v61] Thu, 6 Feb 2025 01:11:23 UTC (418 KB) [v62] Sun, 16 Mar 2025 00:59:18 UTC (423 KB) [v63] Tue, 1 Apr 2025 13:51:22 UTC (426 KB) [v64] Sun, 11 May 2025 11:48:30 UTC (426 KB) [v65] Sun, 1 Jun 2025 04:30:39 UTC (435 KB) [v66] Tue, 1 Jul 2025 12:11:16 UTC (435 KB) [v67] Fri, 1 Aug 2025 06:02:55 UTC (436 KB) [v68] Mon, 1 Sep 2025 14:21:06 UTC (437 KB) [v69] Wed, 1 Oct 2025 04:35:03 UTC (439 KB) [v70] Sat, 1 Nov 2025 23:36:04 UTC (443 KB) [v71] Wed, 7 Jan 2026 09:42:30 UTC (443 KB) [v72] Sun, 1 Feb 2026 05:09:47 UTC (446 KB) [v73] Tue, 3 Mar 2026 00:39:26 UTC (445 KB) [v74] Thu, 2 Apr 2026 00:07:24 UTC (445 KB) [v75] Fri, 1 May 2026 05:23:49 UTC (447 KB) [v76] Wed, 3 Jun 2026 11:07:17 UTC (447 KB) [v77] Wed, 15 Jul 2026 23:01:27 UTC (12,709 KB) [v78] Wed, 22 Jul 2026 03:19:13 UTC (24,826 KB) [v79] Tue, 28 Jul 2026 21:24:15 UTC (24,823 KB) [v80] Tue, 4 Aug 2026 03:13:12 UTC (24,838 KB) [v81] Tue, 11 Aug 2026 13:21:12 UTC (445 KB) [v82] Mon, 24 Aug 2026 14:20:29 UTC (445 KB) [v83] Mon, 31 Aug 2026 12:59:19 UTC (24,838 KB) Full-text links: Access Paper: View a PDF of the paper titled Stochastic Differential Equations: Theory and Practice of Numerical Solution. 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