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
 

Valentin Konakov