Alina Bogoi, Cătălina-Ilinca Dan, Sergiu Strătilă, Grigore Cican, Daniel-Eugeniu Crunteanu
{"title":"Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral","authors":"Alina Bogoi, Cătălina-Ilinca Dan, Sergiu Strătilă, Grigore Cican, Daniel-Eugeniu Crunteanu","doi":"10.3390/sym15112038","DOIUrl":null,"url":null,"abstract":"Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an additional term called “noise” that represents a perturbing factor that cannot be attached to a classical mathematical model. In this paper, we study weak and strong convergence for six numerical schemes applied to a multiplicative noise, an additive, and a system of SDEs. The Efficient Runge–Kutta (ERK) technique, however, comes out as the top performer, displaying the best convergence features in all circumstances, including in the difficult setting of multiplicative noise. This result highlights the importance of researching cutting-edge numerical techniques built especially for stochastic systems and we consider to be of good help to the MATLAB function code for the ERK method.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry-Basel","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym15112038","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an additional term called “noise” that represents a perturbing factor that cannot be attached to a classical mathematical model. In this paper, we study weak and strong convergence for six numerical schemes applied to a multiplicative noise, an additive, and a system of SDEs. The Efficient Runge–Kutta (ERK) technique, however, comes out as the top performer, displaying the best convergence features in all circumstances, including in the difficult setting of multiplicative noise. This result highlights the importance of researching cutting-edge numerical techniques built especially for stochastic systems and we consider to be of good help to the MATLAB function code for the ERK method.
期刊介绍:
Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.