Abstract

Abstract We consider the problem of trend parameter estimation by the observations of ergodic diffusion process in the situation when the trend coefficient of the process is switching, i.e., is discontinuous function of the unknown parameter. In the asymptotics of large samples we prove the consistency of the MLE and Bayes estimators, describe their limiting distributions and show the convergence of moments of these estimators. Then we discuss several generalizations of these results (many jumps, simultaneous estimation of the smooth and discontinuous parameters, multidimentional case and the asymptotics of MLE in misspecified swithching system).

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