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dc.contributor.authorCalatayud, Julia ( Orcid Icon 0000-0002-9639-1530 )
dc.contributor.authorCaraballo, Tomas ( Orcid Icon 0000-0003-4697-898X )
dc.contributor.authorCortes, Juan Carlos ( )
dc.contributor.authorJornet, Marc ( )
dc.identifier.citationCalatayud, J., Caraballo, T., Cortés, J. C., & Jornet, M. (2020). Mathematical methods for the randomized non-autonomous Bertalanffy model. Electronic Journal of Differential Equations, 2020(50), pp. 1-19.en_US

In this article we analyze the randomized non-autonomous Bertalanffy model

x′(t, ω) = α(t, ω)x(t, ω) + b(t, ω)x(t, ω)2/3, x(t0, ω) = x0(ω),

where α(t, ω) and b(t, ω) are stochastic processes and x0(ω) is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on α, b and x0, we obtain a solution stochastic process, x(t, ω), both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loève expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of x(t, ω), ƒx(t)(x). This permits approximating the expectation and the variance of x(t, ω). At the end, numerical experiments are carried out to put in practice our theoretical findings.

dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectRandom non-autonomous Bertalanffy modelen_US
dc.subjectRandom differential equationen_US
dc.subjectRandom variable transformation techniqueen_US
dc.subjectKarhunen-Loeve expansionen_US
dc.subjectProbability density functionen_US
dc.titleMathematical methods for the randomized non-autonomous Bertalanffy modelen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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