Article
Mathematical methods for the randomized non-autonomous Bertalanffy model
Author/s | Calatayud Gregori, Julia
Caraballo Garrido, Tomás Cortés López, Juan Carlos Jornet Sanz, Marc |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2020 |
Deposit Date | 2020-09-08 |
Published in |
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Abstract | In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω)
2/3, x(t0, ω) = x0(ω), where a(t, ω) and b(t, ω) are stochastic processes and x0(ω) is a random ... In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, x(t0, ω) = x0(ω), where a(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 a, 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), fx(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. |
Funding agencies | Ministerio de Economía, Industria y Competitividad (MINECO). España Agencia Estatal de Investigación. España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Universitat Politècnica de València |
Project ID. | MTM2017–89664–P |
Citation | Calatayud Gregori, J., Caraballo Garrido, T., Cortés López, J.C. y Jornet Sanz, M. (2020). Mathematical methods for the randomized non-autonomous Bertalanffy model. Electronic Journal of Differential Equations, 2020 (50), 1-19. |
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