ISI - Filipe, Patrícia A. (2008)
This paper will consider stochastic models for animal growth that take into account the effect on growth of the random fluctuations in the animal’s environment. Let X(t) be the body weight or size of the animal. The traditional deterministic models assume the form of a differential equation dY(t)=b(g(a)-Y(t))dt, where g is a strictly increasing function, Y(t)=g(X(t)), a is the asymptotic size or size at maturity of the animal, and b is the rate of approach to maturity. For instance, the Bertalanffy-Richards model corresponds to g being a power function and the Gompertz model to g being a logarithmic function. In early work we have considered, for animals growing in a random environment, stochastic differential equations models dY(t)=b(g(a)-Y(t))dt+sdW(t), where W(t) is a Wiener process and s measures the intensity of the random environmental fluctuations. We have considered the problems of parameter estimation and prediction for one path. Here we study the extension to several paths, in which case we have data at several time instants coming from several animals. The results and methods are applied to bovine growth data provided by Carlos Roquete (ICAM-University of Évora)