Show simple item record

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.date.accessioned2021-09-29T17:02:27Z
dc.date.available2021-09-29T17:02:27Z
dc.date.issued2020-05-26
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
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14557
dc.description.abstract

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.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
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.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record