A logistic birth-death-immigration-emigration process (Q2744579)

The logistic birth-death-immigration-emigration process \(N(t), t\geq 0, N(0)=0,\) is a continuous time integer-valued processes which represents the size of a population at time \(t\). If \(N(t)=n\), then the infinitesimal probability of an individual birth or immigration during a small interval \(\Delta t\) is \((n\lambda+\alpha) \Delta t ,\) while the infinitesimal probability of a death or emigration occurring during \(\Delta t\) is \((n\mu+n^2\varepsilon) \Delta t\). The author obtains, in terms of a generalized hypergeometric function, explicit formulas for the steady state and moments of the described process.