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 can be both bounded or diverging. The approximation is given in the sense of the Le Cam -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.
DOI : 10.1051/ps/2015005
Mots-clés : Non-parametric experiments, Le Cam distance, asymptotic equivalence, Lévy processes, additive processes, white noise
@article{PS_2015__19__560_0,
author = {Mariucci, Ester},
title = {Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise},
journal = {ESAIM: Probability and Statistics},
pages = {560--577},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2015005},
mrnumber = {3433426},
zbl = {1331.62058},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2015005/}
}
TY - JOUR AU - Mariucci, Ester TI - Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise JO - ESAIM: Probability and Statistics PY - 2015 SP - 560 EP - 577 VL - 19 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2015005/ DO - 10.1051/ps/2015005 LA - en ID - PS_2015__19__560_0 ER -
%0 Journal Article %A Mariucci, Ester %T Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise %J ESAIM: Probability and Statistics %D 2015 %P 560-577 %V 19 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2015005/ %R 10.1051/ps/2015005 %G en %F PS_2015__19__560_0
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. http://www.numdam.org/articles/10.1051/ps/2015005/
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