Quasi-likelihood estimation for semimartingales (Q1821469)

The paper proposes a new technique of parameter estimation for a class of semimartingales, continuous in time, based on a certain type of quasi- likelihood. The class of semi-martingales contains many widely used continuous time stochastic models (e.g. diffusions, Poisson processes and branching processes). The quasi-likelihood to be maximized can be understood as a generalization of the quasi-likelihood introduced by \textit{R. W. M. Wedderburn} [Biometrika 61, 439-447 (1974; Zbl 0292.62050)] in the context of generalized linear models. Consistency and asymptotic normality of the estimator, as well as optimality in the sense of \textit{V. P. Godambe} [see Ann. Math. Stat. 31, 1208-1211 (1960; Zbl 0118.343)], are shown under assumptions which do not rule out nonstationary or non- Markovian behaviour of the process.