Estimation of parameters of linear homogeneous stochastic differential equations
The authors investigate the problem of parametric estimation for multidimensional linear homogeneous differential equations of the form \(dX_t = AX_tdt + \sigma (X_t)dW_t.\) The estimation of the unknown parameter matrix \(A\) using the observations \(X^{(T)}\) of the process \(X_t\), \(0\leq t \leq T\), is considered. They prove the local asymptotic normality property, find the maximum likelihood estimator and prove its asymptotic efficiency for bounded loss functions, when the observation time tends to infinity.
linear stochastic differential equations
scientific article; zbMATH DE number 1409158
scientific article