Two-scale Renormalization Group Classification of Stochastic Processes in Geophysics

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 generated by non-linear clocks and/or infinite second moments. Fixed points of the operators can be used for further subclassification of processes when appropriate limits exist. Several processes are classifed using the renormalization group scheme. Examples to be classifed include advection-diffusion in an ergodic velocity field, and a model of diffusion in the branching network.