Asymptotic properties for a statistical model of an \(\mathbb{R}^d\)-valued Markov chain. (Q1185276)

\textit{I. A. Ibragimov} and \textit{R. Z. Khas'minskij} [Statistical estimation. Asymptotic theory (1981; Zbl 0467.62026)] have established the convergence of statistical experiments for an i.i.d. sequence of real random variables with smooth density. Here the authors generalize the result to a positive recurrent Markov chain with values in \(R^ d\). For related work, see \textit{V. Ya. Levit} [Theory Probab. Appl. 19, 332-346 (1975); translation from Teor. Veroyatn. Primen. 19, 340-354 (1974; Zbl 0334.62033)] and \textit{N. Inagaki} and \textit{Y. Ogata} [Ann. Inst. Stat. Math. 27, 391-419 (1975; Zbl 0381.62023)]. The authors use the Hellinger processes in their study following the work of \textit{J. Jacod} [Stochastic Processes Appl. 32, No. 1, 47-68 (1989; Zbl 0684.60030)].