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This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a Levy driven stochastic differential ...equations whose coefficients are supposed to be known except for the finite-dimensional parameters to be estimated. We suppose that the process is observed under the condition for the rapidly increasing experimental design. By means of the polynomial type large deviation inequality, the mighty convergence of the corresponding statistical random fields is derived, which especially leads to the asymptotic normality at rate of the square root of the terminal sampling time for all the target parameters, and also to the convergence of their moments. In our results, the diffusion coefficient may be degenerate, or even null. Although the resulting estimator is not asymptotically efficient in the presence of jumps, we do not require any specific form of the driving Levy measure, rendering that the proposed estimation procedure is practical and somewhat robust to underlying model specification.show more
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MI2012-2