Parameter estimation for some non-recurrent solutions of SDE

Summary The present paper deals with the problem of parameter estimation for nonlinear stochastic differential equations with solution tending to infinity with time. It is shown that if the trend coefficient is asymptotically linear (like that of an Ornstein-Uhlenbeck process), then the maximum likelihood and trajectory fitting estimators are consistent and asymptotically mixing normal. That is, these estimators behave similar as in the case of a non-ergodic Ornstein-Uhlenbeck process.