Edgeworth-type expansions for transition densities of Markov chains converging to diffusions
Konakov, Valentin ; Mammen, Enno
Bernoulli, Tome 11 (2005) no. 1, p. 591-641 / Harvested from Project Euclid
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We consider triangular arrays of Markov chains that converge weakly to a diffusion process. We prove Edgeworth-type expansions of order o(n-1-δ),δ>0, for transition densities. For this purpose we apply the paramatrix method to represent the transition density as a functional of densities of sums of independent and identically distributed variables. Then we apply Edgeworth expansions to the densities. The resulting series gives our Edgeworth-type expansion for the Markov chain transition density.
Publié le : 2005-08-14
Classification:  diffusion processes,  Edgeworth expansions,  Markov chains,  transition densities 
@article{1126126762,
     author = {Konakov, Valentin and Mammen, Enno},
     title = {Edgeworth-type expansions for transition densities of Markov chains converging to diffusions},
     journal = {Bernoulli},
     volume = {11},
     number = {1},
     year = {2005},
     pages = { 591-641},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1126126762}
}

Konakov, Valentin; Mammen, Enno. Edgeworth-type expansions for transition densities of Markov chains converging to diffusions. Bernoulli, Tome 11 (2005) no. 1, pp.  591-641. http://gdmltest.u-ga.fr/item/1126126762/