A random walk approach to Stochastic Calculus Authors Salim Boukfal Lazaar DOI: 10.2436/20.2002.02.37 Keywords: Brownian motion, random walk, stochastic integral, stochastic differential equation, Langevin. Abstract The aim of this work is to provide an introduction to the subject of Stochastic Calculus. In the first part we talk about the Brownian motion, which we will see that it can be thought as a limit of random walks via Donsker’s Invariance Principle. Next, we heuristically present the stochastic differential equations and see how they can be rigorously defined with the help of the stochastic integral. Finally, we discuss the matter of existence and uniqueness of solutions to such equations and solve a rather simple case like the Langevin equation. Downloads Download data is not yet available. Downloads PDF How to Cite Boukfal Lazaar, S. (2024). A random walk approach to Stochastic Calculus. Reports@SCM, 9(1), 1–9. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154336 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 9 No. 1 (2024) Section Articles License The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.
