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

Published 4 Dec 2014 in math.PR | (1412.1607v1)

Abstract: 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.

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