We consider a sequence of Markov chains weakly convergent to a diffusion. We suppose that a drift term contains a linearly increasing component. The usual parametrix method fails because of this unbounded drift term. We show how to modify the parametrix method to obtain local limit theorems for this case.
Excursions and local limit theorems for Bessel-like random walks
Local limit theorems for smoothed Bernoulli and other convolutions
Error bounds in local limit theorems using Stein's method
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