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

We consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain