Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

Abstract : We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small {\epsilon}. We obtain consistent and asymptotically normal estimators of {\alpha} for fixed {\Delta} and {\epsilon}\rightarrow0 and of ({\alpha},{\beta}) for {\Delta}\rightarrow0 and {\epsilon}\rightarrow0. We compare the estimators obtained with various methods and for various magnitudes of {\Delta} and {\epsilon} based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.
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https://hal.archives-ouvertes.fr/hal-00751549
Contributor : Romain Guy <>
Submitted on : Tuesday, November 13, 2012 - 8:09:54 PM
Last modification on : Thursday, March 21, 2019 - 2:16:52 PM

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  • HAL Id : hal-00751549, version 1
  • ARXIV : 1206.0916

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Romain Guy, Catherine Laredo, Elisabeta Vergu. Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient. 2012. ⟨hal-00751549⟩

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