Abstract
Markov random evolutions and their approximations are analyzed. The main object of study is generators of random processes with independent increments. These processes are considered in Poisson approximation and Levy approximation schemes. Generators of random processes are normalized by parameters that are nonlinear functions. The explicit form of such normalization parameters is shown. The asymptotic representation of generators in both approximation schemes is shown. Normalizing factors of random evolution are presented.
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