Large deviations for random evolutions with independent increments in the scheme of Lévy approximation with split and double merging

Asymptotic analysis of the problem of large deviations for random evolutions with independent increments in the circuit of Lévy approximation with split and double merging is carried out. Large deviations for random evolutions in the circuit of Lévy approximation with split and double merging are determined by the exponential generator for the jumping process with independent increments.