Displaying similar documents to “Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains”

Diffusions with measurement errors. I. Local asymptotic normality

Arnaud Gloter, Jean Jacod (2001)

ESAIM: Probability and Statistics

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We consider a diffusion process X which is observed at times i / n for i = 0 , 1 , ... , n , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance ρ n . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when X is indeed a gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What...

Diffusions with measurement errors. II. Optimal estimators

Arnaud Gloter, Jean Jacod (2001)

ESAIM: Probability and Statistics

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We consider a diffusion process X which is observed at times i / n for i = 0 , 1 , ... , n , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance ρ n . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a gaussian martingale, and we conjecture that they are also optimal in the general case.

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2002)

ESAIM: Probability and Statistics

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In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make...