Mathematical methods for the randomized non-autonomous Bertalanffy model

Abstract

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.