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First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities

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First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities

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Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2022). First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities. AIMS Mathematics. 7(1):1486-1506. https://doi.org/10.3934/math.2022088

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/192071

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Title: First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities
Author: Cortés, J.-C. Navarro-Quiles, A. Romero, José-Vicente Roselló, María-Dolores
UPV Unit: Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny
Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Telecomunicación - Escola Tècnica Superior d'Enginyers de Telecomunicació
Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses
Issued date:
Abstract:
[EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the ...[+]
Subjects: Complex differential equations with uncertainties , Probability density function , Random variable transformation method , Uncertainty quantification , Random models
Copyrigths: Reconocimiento (by)
Source:
AIMS Mathematics. (eissn: 2473-6988 )
DOI: 10.3934/math.2022088
Publisher:
American Institute of Mathematical Sciences
Publisher version: https://doi.org/10.3934/math.2022088
Coste APC: 1000 €
Project ID:
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115270GB-I00/ES/ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONES/
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//AICO%2F2021%2F302//Métodos Computacionales para Ecuaciones Diferenciales Aleatorias. Aplicación a Sistemas Vibratorios/
Thanks:
This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant PID2020-115270GB-I00 ...[+]
Type: Artículo

References

Y. Sibuya, <i>Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation</i>, Rhode Island: American Mathematical Society, vol. 82, 1990.

E. Hille, <i>Ordinary Differential Equations in the Complex Domain</i>, New York: John While &amp; Sons, 1976.

A. Savin, B. Sternin, <i>Introduction to Complex Theory of Differential Equations</i>, Switzerland: Birkhauser Basel, 2017. doi: <a href="http://dx.doi.org/10.1007/978-3-319-51744-5." target="_blank">10.1007/978-3-319-51744-5.</a> [+]
Y. Sibuya, <i>Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation</i>, Rhode Island: American Mathematical Society, vol. 82, 1990.

E. Hille, <i>Ordinary Differential Equations in the Complex Domain</i>, New York: John While &amp; Sons, 1976.

A. Savin, B. Sternin, <i>Introduction to Complex Theory of Differential Equations</i>, Switzerland: Birkhauser Basel, 2017. doi: <a href="http://dx.doi.org/10.1007/978-3-319-51744-5." target="_blank">10.1007/978-3-319-51744-5.</a>

A. Joohy, <i>Ordinary Differential Equations in the Complex Domain with Applications: In Physics and Engineering</i>, Latvia: Scholars' Press, 2018.

I. Laine, <i>Nevanlinna Theory and Complex Differential Equations</i>, Berlin: Walter de Gruyter, 1993. doi: <a href="http://dx.doi.org/10.1515/9783110863147." target="_blank">10.1515/9783110863147.</a>

H. Davis, <i>Introduction to Nonlinear Differential and Integral Equations</i>, Eastford, USA: Martino Fine Books, 2014.

G. Filipuk, A. Lastra, S. Michalik, Y. Takei, H. Zoladeka, <i>Complex Differential and Difference Equations: Proceedings of the School and Conference Held at Bedlewo, Poland, September 2-15, 2018</i>, Walter de Gruyter GmbH and Co KG, 2019.

R. Smith, <i>Uncertainty Quantification: Theory, Implementation, and Applications</i>, ser. Computational Science and Engineering, Philadelphia: SIAM, 2014.

B. Oksendal, <i>Stochastic Differential Equations: An Introduction with Applications</i>, Berlin: Springer, 2007. doi: <a href="http://dx.doi.org/10.1007/978-3-662-03185-8." target="_blank">10.1007/978-3-662-03185-8.</a>

X. Mao, <i>Stochastic Differential Equations and Applications</i>, 2nd ed, New York: Woodhead Publishing, 2007.

T. T. Soong, <i>Random Differential Equations in Science and Engineering</i>, New York: Academic Press, 1973.

T. Neckel, F. Rupp, <i>Random Differential Equations in Scientific Computing</i>, London: Versita, 2013.

C. Braumann, <i>Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance</i>, Wiley, 2019. doi: <a href="http://dx.doi.org/10.1002/9781119166092." target="_blank">10.1002/9781119166092.</a>

D. Xiu, <i>Numerical Methods for Stochastic Computations: A Spectral Method Approach</i>, ser. Computational Science and Engineering, New Jersey: Princeton University Press, 2010. doi: <a href="http://dx.doi.org/10.1515/9781400835348." target="_blank">10.1515/9781400835348.</a>

J. Eriksson, E. Ollila, V. Koivunen, Statistics for complex random variables revisited, <i>Proceedings of the 34th IEEE International Conference on Acoustics, Speech and Signal Processing</i>, (2009), 3565–3568. doi: <a href="http://dx.doi.org/10.1109/ICASSP.2009.4960396." target="_blank">10.1109/ICASSP.2009.4960396.</a>

J. Eriksson, E. Ollila, V. Koivunen, Essential statistics and tools for complex random variables, <i>IEEE T. Signal Proces.</i>, <b>58</b> (2010), 5400–5408. doi: 10.1109/TSP.2010.2054085.

F. D. Neeser, J. L. Massey, Proper complex random processes with applications to information theory, <i>IEEE T. Inform. Theory</i>, <b>29</b> (1993), 1293–1302. doi: 10.1109/18.243446.

A. Khurshid, Z. A. Al-Hemyari, S. Kamal, On complex random variables, <i>Pak. J. Stat. Oper. Res.</i>, <b>8</b> (2012), 645–654. doi: <a href="http://dx.doi.org/10.18187/pjsor.v8i3.534." target="_blank">10.18187/pjsor.v8i3.534.</a>

A. Lapidoth, <i>A Foundation in Digital Communication</i>, Cambridge University Press, 2009.

M. C. Casabán, J. C. Cortés, J. V. Romero, M. D. Roselló, Determining the first probability density function of linear random initial value problems by the Random Variable Transformation (RVT) technique: A comprehensive study, <i>Abstr. Appl. Anal.</i>, <b>2014</b> (2014), 1–25. doi: 10.1155/2013/248512.

J. C. Cortés, A. Navarro-Quiles, J. V. Romero, M. D. Roselló, Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function, <i>Appl. Math. Comput.</i>, <b>331</b> (2018), 33–45. doi: 10.1016/j.amc.2018.02.051.

G. Falsone, D. Settineri, Explicit solutions for the response probability density function of linear systems subjected to random static loads, <i>Probabilist. Eng. Mech.</i>, <b>33</b> (2013), 86–94. doi: 10.1016/j.probengmech.2013.03.001.

G. Falsone, D. Settineri, On the application of the probability transformation method for the analysis of discretized structures with uncertain properties, <i>Probabilist. Eng. Mech.</i>, <b>35</b> (2014), 44–51. doi: 10.1016/j.probengmech.2013.10.001.

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