Richards and Gompertz stochastic growth models with time-varying carrying capacity

Starting from the Richards and the Gompertz deterministic models with time-dependent carrying capacity, we construct some time-inhomogeneous diffusion processes. They are obtained from the solutions of the deterministic differential equations by introducing stochastic perturbations in the cumulative intrinsic intensity function. Some algorithms are formulated and implemented to generate random sample paths of the obtained stochastic processes. The simulated sample paths are used to determine estimates of the mean, standard deviation and coefficient of variation of the processes for several time-dependent increasing carrying capacities. Moreover, from the simulated sample paths we create the histogram and the kernel density estimation, that provide information on the probability density function of Richards and the Gompertz diffusion processes. Various numerical computations are per- formed in the presence of a periodic intrinsic intensity function for various choices of the carrying capacity.