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Working paper

Local limit theorems for Markov chains with trend component of linear growth

arxiv.org. math. Cornell University, 2014. No. 1412.1607v1.
Konakov V., Markova A.
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 theorems for this case.