Abstract: In this paper we develop a general theory for some non-homogeneous density-dependent birth-death processes with special applications to stochastic logistic growth. Approximations to the mean and variance of the logistic process are derived. It is shown that these processes can be closely approximated by diffusion processes. Using this method, new results are developed for approximating the absorption probabilities and the moments of first absorption times for the logistic process.
Key words and phrases: Absorption probability, diffusion process, moments of first absorption time, nonhomogeneous density-dependent birth-death process, stochastic logistic growth.