Least squares estimators for stochastic differential equations with Markovian switching

Abstract

This work focuses on the parameter estimation for a class of switching diffusion processes which contains a continuous component and a discrete component. Under suitable conditions, we adopt the least square method to deal with the parameter estimation of stochastic differential equations with Markovian switching. More precisely, we first prove the consistency and the asymptotic distributions of the parameter estimator of least squares when $ \varepsilon\rightarrow0 $ and $ \Delta\rightarrow0 $. Then, we present an example of numerical simulation to illustrate the correctness of the results.