1/f Fluctuations on a Chain of Causal Relationships (Ⅰ); Formalization

In order to discuss the 1⁄f problem, the statistics of the branching process of a particle in a multiplicative medium is developed by taking into account random particle immigration. The probability distribution function of the number of particles found in the medium at any fixed time and/or of particles detected in a time interval is obtained in closed form. These results are applied to the case where exactly two particles are produced by branching.