摘要
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.
基金
This work was substantially supported by the National Natural Science Foundation of China(Grant Nos.11771452,11971486)
the Natural Science Foundation of Hunan(No.2020JJ4674).
