SOME TIME RANDOM VARIABLES RELATED TO A GOMPERTZ-TYPE DIFFUSION PROCESS

In the context of a Gompertz-type diffusion process (associated with a particular expression of the Gompertz curve for which its limit value depends on the initial value), we consider the study of two time-random variables: the inflection time of the model and the time at which it achieves a certain percentage of the total growth. Once we have shown the difficulties in the approach of the former, we deal with it as a particular case of the second. Furthermore, because of the peculiar characteristics of the considered process, we prove that these two problems can be formulated as a first-passage-time problem through a constant boundary. Finally, we conclude with an application to the growth of rabbits, in which we obtain the density functions of the inflection time and the time at which a rabbit achieves the half of its total growth.

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