1/f Noise: Branching Process Model (I); Formalization

EasyChair Preprint 996, version 2

Abstract

In order to discuss the  problem, the statistics of branching process of particle in a multiplicative medium are developed by taking account of random particle immigration.  The probability distribution function of the number of particles founded in the medium at a moment and/or of particles detected in a time interval are derived in close forms.  Also derived are conditional probabilities, conditioned on having a given number of particles at time t=0.  These are applied to the case that exactly two particles are produced by branching.

Keyphrases: 1/f noise, brancching process, formalization, probability

@booklet{EasyChair:996,
  author    = {Takayuki Kobayashi},
  title     = {1/f Noise: Branching Process Model (I); Formalization},
  howpublished = {EasyChair Preprint 996},
  year      = {EasyChair, 2020}}