Estimation of intrinsic growth factors in a class of stochastic population model

Abstract

This article discusses the problem of parameter estimation with nonlinear mean-reversion type stochastic differential equations (SDEs) driven by Brownian motion for population growth model. The estimator in the population model is the climate effects, population policy and environmental circumstances which affect the intrinsic rate of growth r. The consistency and asymptotic distribution of the estimator θ is studied in our general setting. In the calculation method, unlike previous study, since the nonlinear feature of the model, it is difficult to obtain an explicit formula for the estimator. To solve this, some criteria are used to derive an asymptotically consistent estimator. Furthermore Girsanov transformation is used to simplify the equations, which then gives rise to the corresponding convergence of the estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure.