On the simulation of continuous in scale universal multifractals, part I: Spatially continuous processes

摘要

In Part I we considered continuous in scale cascade processes which were spatially continuous; these are needed for modeling many geoflelds. In this second part we consider the effects of spatial discretization; this allows us to make numerical simulations. We show how to correct the simulations for the leading finite size effects, for both space and (causal) space-time processes. The resulting processes have significantly improved small scale statistical properties; in practice it can lead to great savings in computer time and memory usage. In an appendix we give a Mathematical code for the corresponding space-time simulations.