Estimation for nonlinear stochastic differential equations by a local linearization method¹

Abstract

This paper proposes a new local linearization method which approximates a nonlinear stochastic differential equation by a linear stochastic differential equation. Using this method, we can estimate parameters of the nonlinear stochastic differential equation from discrete observations by the maximum likelihood technique. We conduct the numerical experiments to evaluate the finite sample performance of identification of the new method, and compare it with the two known methods: the original local linearization method and the Euler methods. From the results of experiments, the new method shows much better performance than the other two methods particularly when the sampling interval is large