For Markov chains with unbounded, at most linearly growing drift converging to a diffusion, the paper claims a pointwise transition-density error bound of order n^{-min(γ/2,α,β)} plus coefficient discrepancies, times polynomial weight and a logarithm.
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Asymptotic version of the parametrix method for Markov chains converging to diffusions
For Markov chains with unbounded, at most linearly growing drift converging to a diffusion, the paper claims a pointwise transition-density error bound of order n^{-min(γ/2,α,β)} plus coefficient discrepancies, times polynomial weight and a logarithm.