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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 Department of Economics

Abstract : We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of order $on^{-1-\delta},\delta>0,$ 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 : transition densities Edgeworth expansions Markov chains diffusion processes





Autor: Vladimir Konakov - Enno Mammen -

Fuente: https://hal.archives-ouvertes.fr/



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