ANISOTROPIC SCALING OF RANDOM FIELDS WITH LONG-RANGE DEPENDENCE: SCALING LIMITS OF RANDOM FIELDS WITH APPLICATIONS

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker’s theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales.

In the case of a random field indexed by a two-dimensional parameter, both types of scaling can be a…