Abstract
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.
Citation
Valentin Konakov. Enno Mammen. "Edgeworth-type expansions for transition densities of Markov chains converging to diffusions." Bernoulli 11 (4) 591 - 641, Aug 2005. https://doi.org/10.3150/bj/1126126762
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