Stochastic differential equation models and their applications to agriculture: An overview

Abstract

Nonlinear growth models play a very important role in almost all disciplines. The current status of applying them to data is to first assume an additive error in the model and then employing nonlinear estimation procedures. In this article, limitations of this methodology are highlighted. It is advocated that, for a more realistic modeling, a stochastic term should be added to the differential equation form of a growth model, thereby yielding a stochastic differential equation (SDE) growth model. A brief description is provided of the two types of stochastic calculi due respectively to Stratonovich and Ito. The methodologies for application of several univariate growth models, viz. Gompertz, Richards, von Bertalanffy and generalized logistic SDE models are described. Some work dealing with bivariate SDE growth models is also discussed. Finally, some future research problems in the area are outlined.