Processing of Fractal Functions by Linear and Nonlinear Operators

摘要

A method for predicting the stochastic response of systems, or operators, to fluctuating inputs is presented. The inputs are represented by a multiple-scale model which combines concepts of fractal geometry with a resolution into minimum-uncertainty cells. Associated probability distributions are expressed in terms of generalized or Gibbs energy functions. System, or operator, response may be linear or nonlinear and is evaluated by a functional-integral technique based on the Laplace asymptotic approximation.