SEQUENTIAL MAXIMUM LIKELIHOOD ESTIMATION IN NONLINEAR NONMARKOV DIFFUSION TYPE PROCESSES

We obtain the strong consistency, uniform asymptotic normality and local asymptotic minimaxity (in the Hajek-LeCam sense) of the two stage sequential maximum likelihood estimator of a parameter appearing nonlinearly in the drift coefficient of a stochastic differential equation when the corresponding non-Markov diffusion type process is observed until the observed Fisher information of the process exceeds a predetermined level of precision and the level becomes large. Main results are illustrated by the exponential memory non-Markovian Ornstein-Uhlenbeck
process.