Down/up crossing properties of weighted Markov collision processes

Abstract

This paper concentrates on considering the down/up crossing property of weighted Markov collision processes. The joint probability generating function of down crossing and up crossing numbers of weighted Markov collision processes until its extinction are obtained by constructing and studying a related multi-dimensional Markov chain. Hence, the joint probability distribution of down crossing and up crossing numbers and the mean numbers are obtained.

Key words： Weighted Markov collision process; down crossing; up crossing; joint probability distribution

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