Bernoulli

  • Bernoulli
  • Volume 7, Number 6 (2001), 899-912.

Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach

Emmanuel Gobet

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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.

Article information

Source
Bernoulli, Volume 7, Number 6 (2001), 899-912.

Dates
First available in Project Euclid: 10 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1078951128

Mathematical Reviews number (MathSciNet)
MR1873834

Zentralblatt MATH identifier
1003.60057

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

Citation

Gobet, Emmanuel. Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach. Bernoulli 7 (2001), no. 6, 899--912. https://projecteuclid.org/euclid.bj/1078951128


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