Estimation for the change point of volatility in a stochastic differential equation

Abstract: We consider a multidimensional Itô process with some unknown drift coefficient process and volatility coefficient with covariate process , the function being known up to . For this model, we consider a change point problem for the parameter in the volatility component. The change is supposed to occur at some point . Given discrete time observations from the process , we propose quasi-maximum likelihood estimation of the change point. We present the rate of convergence of the change point estimator and the limit theorems of the asymptotically mixed type. [Copyright &y& Elsevier]