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We consider the Markov random evolutions and their approximations. These evolutions are considered in Poisson approximation and Lévy approximation scheme. The main object of study is the exponential generator of random processes with independent increments. Generators of random evolutions are normalized by parameters, which are nonlinear functions.

The Problem of Large Deviations for Markov Evolutions in the Scheme of Poisson and Lévy Approximation