Stationary Densities and Parameter Estimation for Delayed Stochastic Logistic Growth Laws with Application in Biomedical Studies

Abstract

The study of nonlinear stochastic delayed process is significant for understanding nature of complex system in reductionistic viewpoints. This paper investigates the stochastic linear and logistic (Verhulst, Gompertz and Richards) models, and simulates the growth process of Ehrilch ascities tumor (EAT) in a mouse. In order to explain the oscillations of EAT growth we use a system of stochastic differential equations with time delay. We derive the exact and approximate stationary densities in the case of small time delays. For the estimation of parameters we propose the L1 distance and maximum likelihood procedures. As an illustrative experience we use a real data set from repeated measurements on Ehrilch ascities tumor in a mouse. The results are implemented in the symbolic computational language MAPLE.