Geodesic
Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise
Mariucci, Ester1 
1 Laboratoire Jean Kuntzmann, 51 rue des Mathématiques, 38041 Grenoble cedex 09, France.
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 560-577

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We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here, the parameter of interest is the drift function and the observation time T can be both bounded or diverging. The approximation is given in the sense of the Le Cam Δ-distance, under some smoothness conditions on the unknown drift function. These asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.

Reçu le :
DOI : 10.1051/ps/2015005
Classification : 62B15, 62G20, 60G51, 62C20
Keywords: Non-parametric experiments, Le Cam distance, asymptotic equivalence, Lévy processes, additive processes, white noise

Mariucci, Ester 1

1 Laboratoire Jean Kuntzmann, 51 rue des Mathématiques, 38041 Grenoble cedex 09, France. 
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     title = {Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise},
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Mariucci, Ester. Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 560-577. doi: 10.1051/ps/2015005

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