A theory of noise based on generalized random walks

Based on a generalized random walks (GRW) model proposed by one of the present authors, a theory of noise is developed. In the present system, two different types of randomness, internal and external, are considered. Internal noises yield the ususal randomness for a walker and lead one to a description based on random walks. External noises appear as additional fluctuations around the original processes. Jumping probabilities are composed of the corresponding two types of randomness. It is shown that a specification of these jumping reduces the present basic equation to the expression used in the conventional noise theory.