Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points
In this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second probability density functions of the solution stochastic process are computed. Then, the main statistical functions, namely, the mean, the variance a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2017-06-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.21042/AMNS.2017.1.00018 |
| _version_ | 1818308746282008576 |
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| author | Cortés J.-C. Navarro-Quiles A. Romero J.-V. Roselló M.-D. |
| author_facet | Cortés J.-C. Navarro-Quiles A. Romero J.-V. Roselló M.-D. |
| author_sort | Cortés J.-C. |
| collection | DOAJ |
| description | In this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second probability density functions of the solution stochastic process are computed. Then, the main statistical functions, namely, the mean, the variance and the covariance functions are determined as well. The study includes the computation of the first and second probability density functions of the regular-singular infinite point via an adequate mapping transforming the problem about the origin. The study is strongly based upon the Random Variable Transformation technique along with some results that have been recently published by some of authors to the random homogeneous linear second-order differential equation. Finally, an illustrative example is shown. |
| first_indexed | 2024-12-13T07:19:10Z |
| format | Article |
| id | doaj.art-c908856e166142959fbca0056c0f6c30 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-13T07:19:10Z |
| publishDate | 2017-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-c908856e166142959fbca0056c0f6c302022-12-21T23:55:28ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562017-06-012121322410.21042/AMNS.2017.1.00018Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular pointsCortés J.-C.0Navarro-Quiles A.1Romero J.-V.2Roselló M.-D.3Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, SpainIn this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second probability density functions of the solution stochastic process are computed. Then, the main statistical functions, namely, the mean, the variance and the covariance functions are determined as well. The study includes the computation of the first and second probability density functions of the regular-singular infinite point via an adequate mapping transforming the problem about the origin. The study is strongly based upon the Random Variable Transformation technique along with some results that have been recently published by some of authors to the random homogeneous linear second-order differential equation. Finally, an illustrative example is shown.https://doi.org/10.21042/AMNS.2017.1.00018random cauchy-euler differential equationrandom variable transformation techniquefirst and second probability density functions35r6060h1560h3568u20 |
| spellingShingle | Cortés J.-C. Navarro-Quiles A. Romero J.-V. Roselló M.-D. Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points Applied Mathematics and Nonlinear Sciences random cauchy-euler differential equation random variable transformation technique first and second probability density functions 35r60 60h15 60h35 68u20 |
| title | Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points |
| title_full | Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points |
| title_fullStr | Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points |
| title_full_unstemmed | Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points |
| title_short | Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points |
| title_sort | computing the two first probability density functions of the random cauchy euler differential equation study about regular singular points |
| topic | random cauchy-euler differential equation random variable transformation technique first and second probability density functions 35r60 60h15 60h35 68u20 |
| url | https://doi.org/10.21042/AMNS.2017.1.00018 |
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