Lévy approximation of an impulse recurrent process with Markov switching
Анотація
The weak convergence of an impulse recurrent process with Markov switching is proved in this paper for the scheme of the Lévy approximation. A modified Liptser semimartingale method is applied to the proof of the relative compactness of the process under consideration. The modification of the Liptser method used in the paper relies upon a solution of a singular perturbation problem instead of an ergodic theorem as used in the original Liptser method.
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