Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60F99 None of the above but in this section
- 60J75 Jump processes
- 62A10 The likelihood approach

**Résumé:** We consider here a sequence of parametric models
associated with the observation at times $i/n,~1\le i\le n$ of the
solution to the equation $~dX_t=\vth~[dW_t+f(X_{t^-})dY_t],~$ where
$\vth$ is an unknown parameter. $W$ is a standard Brownian motion and
$Y$ is a compound Poisson with L\'evy measure $F$ having no singular
diffuse part. Under some regularity assumptions on $f$, we prove a
convergence theorem for the sequence of local density processes of
$P^{\tnh}$ with respect to $P^\vth.~$
A corollary of this result is the LAMN property in the case $f=1,$
providing an asymptotic lower bound for the variance of the
estimation. We give also some sequences of estimators achieving this
lower bound.

**Mots Clés:** *Local asymptotic mixed normality ; stable convergence in law ; limit theorem for semimartingale*

**Date:** 2000-06-16

**Prépublication numéro:** *PMA-600*