Noise associated with reduction, multiplication and branching processes

We consider noise in particle fluxes which undergo a reduction or a multiplication process, either direct or via branching. It is shown that these processes can be described with the method of addition of independent events, or with a collective procedure. Using the statistical rules for compound and branching processes, general results for the variance of these processes are obtained. In particular, we consider the reduction process associated with the Bernouilli trials, the multiplication process due to geometric variables, some branching processes, and the combined multiplication-reduction process. The results are applied to various cases, such as secondary emission noise, avalanche noise in low voltage breakdown diodes (zener diodes) and in JFETs, cathodoluminescence, noise and interval statistics.