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Regular version of the site

Article

Local limit theorems for transition densities of Markov chains converging to diffusions

Probability Theory and Related Fields. 2000. Vol. 117. No. 4. P. 551-587.
Konakov V., Mammen E.

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved.