THE PARAMETER ESTIMATION OF FREQUENCY WITH WHITE NORSE

Suppose a stochastic process X_T=X（t）:0≤t≤Tsatisfces following equation:X(t)=\int_0^t \sin \theta s d s+W(t) \quad 0 \leqslant t \leqslant T where W_T=W（t）,t∈T is a standard Wiener process. In this paper we study the properties of the MLE of the parameter θ in signal \int \sin \theta s d s. We obtained strong consistence, asymptotical normality and a.s convergence rate of the parameter estimation in the unbounded parameter space.