Abstract. The methods proposed in the paper allow us to investigate the model of stochatic evolution, which includes Markov switchings, and to identify big jumps of disturbing process in the limiting equation. Big jumps of this type may describe rare catastrophic events in different applied problems. We consider the case where system disturbance is defined by impulse process in nonclassical approximation scheme. Particular attention is paid to the asymptotic behavior of the generator of the evolutionary system under examination.

Keywords: stochastic diffusion equation, generator on Banaсh space, Markov process, stochastic approximation procedure, Poisson approximation.