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December 2001 Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach
Emmanuel Gobet
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Bernoulli 7(6): 899-912 (December 2001).

Abstract

We address the problem of the validity of the local asymptotic mixed normality (LAMN) property when the model is a multidimensional diffusion process X whose coefficients depend on a scalar parameter θ: the sample (Xk/n)0≤ k≤ n corresponds to an observation of X at equidistant times in the interval [0,1]. We prove that the LAMN property holds true for the likelihood under an ellipticity condition and some suitable smoothness assumptions on the coefficients of the stochastic differential equation. Our method is based on Malliavin calculus techniques: in particular, we derive for the log-likelihood ratio a tractable representation involving conditional expectations.

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Emmanuel Gobet. "Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach." Bernoulli 7 (6) 899 - 912, December 2001.

Information

Published: December 2001
First available in Project Euclid: 10 March 2004

zbMATH: 1003.60057
MathSciNet: MR1873834

Keywords: conditional expectation , convergence of sums of random variables , diffusion process , local asymptotic mixed normality property , log-likelihood ratios , Malliavin calculus , Parametric estimation

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

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Vol.7 • No. 6 • December 2001
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