ASYMPTOTIC INFERENCE FOR MARKOV STEP PROCESSES - OBSERVATION UP TO A RANDOM TIME

Consider a Markov step process whose generator depends on an unknown o ne-dimensional parameter theta. Under a 'homogeneity' assumption conce rning the family of information processes I(theta), theta is-an-elemen t-of THETA, which does not require exact knowledge of the asymptotics of I(theta) under P(theta) there is an increasing sequence of bounded stopping times U(n) such that, observing X continuously over the rando m time interval [[0, U(n)]], the sequence of resulting statistical mod els is LAN as n --> infinity, at every point theta is-an-element-of TH ETA, with local scale which does not depend on the parameter.