• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Edgeworth type expansions for transition densities of Markov chains converging to diffusions

Konakov V., Mammen E.

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 parametrix 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.