A weight Monte Carlo estimation of fluctuations in branching processes

It is well known that shortened modeling of particle trajectories with the use multiplicative statistical weights, as a rule, increases the efficiency of the program (in terms of accuracy/time ratio). This trick is often used in non-branching schemes simulating transfer processes without multiplication (for example, the transfer of X-ray radiation), in which it is sufficient to confine ourselves to studying only the average values of the field characteristics. With an increase in energy, however, multiplication processes begin to play a significant role (the production of electron-photon pairs by gamma quanta with energies above 1.022 MeV, etc.), when the resulting trajectory is not just a broken curve in the phase space, but a branched tree. This technique is also applicable to this process, but only if the study of statistical fluctuations and correlations is not the purpose of the calculation. The present review contains the basic concepts of the Monte Carlo method as applied to the theory of particle transport, demonstration of the weighting method in non-branching processes, and ends with a discussion of unbiased estimates of the second moment and covariance of additive functionals.