(Received May 8, 1996; revised June 10, 1997)
Abstract. Consider a Markov step process X = (Xt)t >0 whose generator depends on an unknown parameter vartheta. We are interested in estimation of vartheta by a class of minimum distance estimators (MDE) based on observation of X up to time Sn, with (Sn)n a sequence of stopping times increasing to \infty. We give a precise description of the MDE error at stage n, for n fixed, i.e. a stochastic expansion in terms of powers of a norming constant and suitable coefficients (which can be calculated explicitly from the observed path of X up to time Sn).
Key words and phrases: Markov step processes, minimum distance estimators, stochastic expansions.
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