The “No Sampling Parameter Estimation (NSPE)” algorithm for stochastic differential equations

Abstract

The parameter estimation problem in stochastic differential equations (SDEs) has gained much attention in recent years due to their increased applications in the field of pharmaceuticals, ecosystem modeling, and medical data like EKG, blood pressure, and sugar levels. The predictive power of SDEs lie in the choice of parameter values that describe the real data effectively. The classical SDE parameter estimation methods are largely based on likelihood estimation, which is computationally expensive. In this work, we propose a relatively simplified approach based on deterministic nonlinear optimization method which does not require sampling. The results from the suggested No Sampling Parameter Estimation (NSPE) algorithm for selected examples are compared with the data, results from deterministic ODE (ordinary differential equation) model and traditional methods of maximum likelihood estimation (MLE) and generalized method of moments (GMM) for SDEs. The NSPE algorithm is more accurate and reduces computation time significantly when compared to the traditional methods.