Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Edgeworth type expansions for transition densities of Markov chains converging to diffusions

Auteur(s):

Code(s) de Classification MSC:

• 62G07 Density estimation
• 60G60 Random fields

Résumé: We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of order $o(n^{-1-\delta}),\delta>0,$ for transition densities are proved. For this purpose we represent the transition density as a functional of densities of sums of i.i.d. variables. This will be done by application of the parametrix method. Then we apply Edgeworth expansions to the densities. The resulting series gives our Edgeworth-type expansion for the transition density of Markov chain.

Mots Clés: Markov chains ; diffusion processes ; transition densities ; Edgeworth expansions

Date: 2004-07-09

Prépublication numéro: PMA-923