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Local limit theorems for transition densities of Markov chains converging to diffusions. (English) Zbl 0996.60083
The authors consider triangular arrays of Markov chains that converge weakly to a diffusion process and prove local limit theorems for transition densities using an analytical approach. They apply the parametrix method for parabolic pde’s and a modification of this method for discrete time Markov processes.

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
62G07 Density estimation
60F05 Central limit and other weak theorems
60J60 Diffusion processes
35K55 Nonlinear parabolic equations
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