Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral
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 pert...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/2038 |
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| author | Alina Bogoi Cătălina-Ilinca Dan Sergiu Strătilă Grigore Cican Daniel-Eugeniu Crunteanu |
| author_facet | Alina Bogoi Cătălina-Ilinca Dan Sergiu Strătilă Grigore Cican Daniel-Eugeniu Crunteanu |
| author_sort | Alina Bogoi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T16:25:03Z |
| format | Article |
| id | doaj.art-e2d50b81a05a466885863e0c2b18ac44 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:25:03Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e2d50b81a05a466885863e0c2b18ac442023-11-24T15:08:51ZengMDPI AGSymmetry2073-89942023-11-011511203810.3390/sym15112038Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s IntegralAlina Bogoi0Cătălina-Ilinca Dan1Sergiu Strătilă2Grigore Cican3Daniel-Eugeniu Crunteanu4Faculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, RomaniaFaculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, RomaniaFaculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, RomaniaFaculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, RomaniaFaculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, RomaniaStochastic 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.https://www.mdpi.com/2073-8994/15/11/2038stochasticItôwhite noiseGaussian distributionWiener processconvergence |
| spellingShingle | Alina Bogoi Cătălina-Ilinca Dan Sergiu Strătilă Grigore Cican Daniel-Eugeniu Crunteanu Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral Symmetry stochastic Itô white noise Gaussian distribution Wiener process convergence |
| title | Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral |
| title_full | Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral |
| title_fullStr | Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral |
| title_full_unstemmed | Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral |
| title_short | Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral |
| title_sort | assessment of stochastic numerical schemes for stochastic differential equations with white noise using ito s integral |
| topic | stochastic Itô white noise Gaussian distribution Wiener process convergence |
| url | https://www.mdpi.com/2073-8994/15/11/2038 |
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