Two-scale renormalization-group classification of diffusive processes

Abstract

Renormalization-group operators are used to classify stochastic processes on two time scales. Repeated application of one operator is associated with the long-time behavior of the process while the other is associated with the short-time behavior of the process. This approach is shown to be robust even in the presence of nonstationary increments and infinite second moments. Fixed points of the operators can be used for further subclassification of processes when appropriate limits exist. Several processes are classified using the renormalization-group scheme. The processes to be classified include advection-diffusion in an ergodic velocity field, and a model of diffusion in the human bronchial tree.