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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

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

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Code(s) de Classification MSC:

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