Small time asymptotics in local limit theorems for Markov chains   converging to diffusions
  We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved. The observation time [0,T] may be fixed or lim n T = 0, where nh = T and h is a mesh between two neighboring observation points. 
Valentin Konakov