Mathematical methods for the randomized non-autonomous Bertalanffy model

In this article we analyze the randomized non-autonomous Bertalanffy modelwhere  and  are stochastic processes and  is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and , we obtain a solution stochastic process, , both in the sa...

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Bibliographic Details
Published in:Electronic journal of differential equations 2020-05, Vol.2020 (1-132), p.50
Main Authors: Calatayud, Julia, Caraballo, Tomas, Cortes, Juan Carlos, Jornet, Marc
Format: Article
Language:English
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Summary:In this article we analyze the randomized non-autonomous Bertalanffy modelwhere  and  are stochastic processes and  is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and , we obtain a solution stochastic process, , both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of , . This permits approximating the expectation and the variance of . At the end, numerical experiments are carried out to put in practice our theoretical findings.
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2020.50