Weighted estimate of the Monte-Carlo method for calculating the higher moments of the additive transport characteristics of multiplying particles

A closed Integral representation is given for a moment of an arbitrary order of an arbitrary additive stochastic characteristic of a cascade process involving the transport of particles in a substance. An unbiased non-simulation estimate of the Monte-Carlo method is proposed for calculating such moments on the trajectories of a branching Markov process with discrete time. An example of the efficient use of the estimate is given.