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.

Keywords:

• Population growth model
• intrinsic rate of growth
• environmental factors
• nonlinear mean-reversion type SDEs
• Girsanov transformation
• least square estimator (LSE)
• discrete observation
• consistency of least square estimator
• asymptotic distribution of LSE

MSC(2010):

• 60H10
• 62F12
• 62M05

Disclosure statement

No potential conflict of interest was reported by the authors.

Note on contributors

All authors have made equal contributions. All authors have read and approved the final article.

Additional information

Funding

This research was supported by Tianjin Municipal Education Commission Scientific Research Project of China Research on the construction of environmental credit evaluation system for textile enterprises under the background of big data (Grant No. 161082).