Article

# Accuracy of Diffusion Approximations for High Frequency Markov Data

03/2006;
Source: arXiv

ABSTRACT We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of third order for transition densities are proved. This is done for time horizons that converge to 0. 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 chains. The research is motivated by applications to high frequency data that are available on a very fine grid but are approximated by a diffusion model on a more rough grid.

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### Keywords

available

converge weakly

Edgeworth type expansions

Edgeworth-type expansion

fine grid

frequency data

parametrix method

resulting series

rough grid

sums

third order

time horizons

transition densities

transition density

triangular arrays