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We consider the diffusion process and its approximation by Markov chain withnonlinear increasing trends. The usual parametrix method is not appliablebecause these models have unbounded trends. We describe a procedure that allowsto exclude nonlinear growing trend and move to stochastic differential equationwith reduced drift and diffusion coefficients. A similar procedure isconsidered for a Markov chain

The procedure of excluding of the nonlinear trend fir the models described by stochastic differential and difference equations