Edgeworth type expansions for transition densities of Markov chains converging to diffusions
Konakov, Vladimir ; Mammen, Enno
HAL, hal-00002984 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-09-30
Classification:  transition densities,  Edgeworth expansions,  Markov chains,  diffusion processes,  62G07 60G60,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00002984,
     author = {Konakov, Vladimir and Mammen, Enno},
     title = {Edgeworth type expansions for transition densities of Markov chains converging to diffusions},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00002984}
}

Konakov, Vladimir; Mammen, Enno. Edgeworth type expansions for transition densities of Markov chains converging to diffusions. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002984/