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

2014/12/04 by V.D. Konakov, V. Konakov, Konakov, V. +2
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1412.1607

arxiv created 2014/12/04 · arxiv updated 2014/12/05

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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