Mean number of joint jumps of multivariate extremes of particle scores in Markov branching processes. Clayton copula case

The paper continues the long-term studies of the authors on the extremes of random particles scores in branching processes. A theorem is proved that allows one to find the mean number of joint jumps of multivariate maxima of particle scores in Markov branching processes with continuous time, including processes with immigration. Examples are analyzed where the dependence of scores is described by Clayton copula.