{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:38:38Z","timestamp":1760243918592,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2010,7,1]],"date-time":"2010-07-01T00:00:00Z","timestamp":1277942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This brief note presents an algorithm to solve ordinary stochastic differential equations (SDEs). The algorithm is based on the joint solution of a system of two partial differential equations and provides strong solutions for finite-dimensional systems of SDEs driven by standard Wiener processes and with adapted initial data. Several examples illustrate its use.<\/jats:p>","DOI":"10.3390\/a3030216","type":"journal-article","created":{"date-parts":[[2010,7,1]],"date-time":"2010-07-01T10:01:43Z","timestamp":1277978503000},"page":"216-223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithmic Solution of Stochastic Differential Equations"],"prefix":"10.3390","volume":"3","author":[{"given":"Henri","family":"Schurz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Southern Illinois University, 1245 Lincoln Drive, Carbondale, IL 62901, USA"}]}],"member":"1968","published-online":{"date-parts":[[2010,7,1]]},"reference":[{"key":"ref_1","unstructured":"Allen, E. (2008). Modeling with It\u00f4 Stochastic Differential Equations, Springer-Verlag."},{"key":"ref_2","unstructured":"Arnold, L. (1974). Stochastic Differential Equations, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Friedman, A. (1975\/1976). Stochastic Differential Equations and Applications 1 & 2, Academic Press.","DOI":"10.1016\/B978-0-12-268201-8.50006-2"},{"key":"ref_4","unstructured":"Gard, T.C. (1988). Introduction to Stochastic Differential Equations, Marcel Dekker."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gikhman, I.I., and Skorochod, A.V. (1971). Stochastische Differentialgleichungen, Akademie-Verlag.","DOI":"10.1515\/9783112727393"},{"key":"ref_6","first-page":"519","article-title":"Stochastic integral","volume":"20","year":"1944","journal-title":"Proc. Imp. Acad. Tokyo"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1017\/S0027763000012216","article-title":"On a formula concerning stochastic differential equations","volume":"3","year":"1951","journal-title":"Nagoya Math. J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Karatzas, I., and Shreve, S. (1988). Brownian Motion and Stochastic Calculus, Springer-Verlag.","DOI":"10.1007\/978-1-4684-0302-2"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Krylov, N.V. (1995). Introduction to the Theory of Diffusion Processes, AMS.","DOI":"10.1090\/mmono\/142"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"\u00d8ksendal, B. (1985). Stochastic Differential Equations, Springer-Verlag.","DOI":"10.1007\/978-3-662-13050-6"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Protter, P. (1990). Stochastic Integration and Differential Equations, Springer-Verlag.","DOI":"10.1007\/978-3-662-02619-9"},{"key":"ref_12","unstructured":"Revuz, D., and Yor, M. (1994). Continuous Martingales and Brownian Motion, Springer-Verlag. [2nd ed.]."},{"key":"ref_13","first-page":"241","article-title":"Stochastic \u03b1-calculus, a fundamental theorem and Burkholder-Davis-Gundy-type estimates","volume":"15","author":"Schurz","year":"2006","journal-title":"Dynam. Syst. Applic."},{"key":"ref_14","first-page":"181","article-title":"New stochastic integrals, oscillation theorems and energy identities","volume":"13","author":"Schurz","year":"2009","journal-title":"Commun. Appl. Anal."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shiryaev, A.N. (1996). Probability, Springer-Verlag. [2nd ed.].","DOI":"10.1007\/978-1-4757-2539-1"},{"key":"ref_16","unstructured":"Stroock, D.W., and Varadhan, S.R.S. (1982). Multidimensional Diffusion Processes, Springer-Verlag."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/216\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:49Z","timestamp":1760220169000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,1]]},"references-count":16,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2010,9]]}},"alternative-id":["a3030216"],"URL":"https:\/\/doi.org\/10.3390\/a3030216","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2010,7,1]]}}}