Mathematical methods for the randomized non-autonomous Bertalanffy model

Abstract

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

x' (t, omega) = a(t, omega)x(t, omega) b(t, omega)x(t, omega)(2/3), x(t(0), omega) = x(0)(omega),

where a(t, omega) and b(t, omega) are stochastic processes and x(0)(omega) is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and x(0), we obtain a solution stochastic process, x(t, omega), 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 x(t, omega), f (t) (x). This permits approximating the expectation and the variance of x(t, omega). At the end, numerical experiments are carried out to put in practice our theoretical findings.