Ingemar Nåsell: An alternative to cumulant closure

An alternative to the cumulant closure method for the stochastic logistic model is described. It leads to asymptotic approximations of the first few cumulants of the quasi-stationary distribution in the parameter region where the time to extinction is long. Compared with the cumulant closure method, it has the advantages that a condition for validity of the approximation is known, that the magnitude of the error associated with the approximation can be determined, that a simple analytical form of the approximation is given, and that the nuisance of dealing with spurious solutions is eliminated.