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


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.


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Valentin Konakov. Enno Mammen. "Edgeworth-type expansions for transition densities of Markov chains converging to diffusions." Bernoulli 11 (4) 591 - 641, Aug 2005.


Published: Aug 2005
First available in Project Euclid: 7 September 2005

zbMATH: 1098.60069
MathSciNet: MR2158253
Digital Object Identifier: 10.3150/bj/1126126762

Keywords: Diffusion processes , Edgeworth expansions , Markov chains , transition densities

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 4 • Aug 2005
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