Donatas Surgailis

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

Anisotropic Scaling of Random Fields with Long-Range Dependence is primarily interested in two questions: are there scaling limits for all γ>0 ratios? And if so, what are they? By introducing the concept of a scaling transition and discussing its existence for Gaussian models, moving-average models, and their subordinated planar models, the very cutting-edge of research and theory within scaling transition is explored, interrogated, and understood.If a scaling parameter tends to zero or infinity (infinite scaling), this can lead to a limit which is self-similar and much simpler than the original object. In the case of a random field indexed by a two-dimensional, both types of scaling can be anisotropic - meaning that the horizontal and vertical axes are scaled at different rates determined by the ratio γ>0 of the scaling exponents along the axes. Within this text, a wide class of linear and nonlinear random fields are analysed through the critically underdiscussed concept of a scaling transition. A central engagement of this research involves joint temporal and contemporaneous aggregation of spatio-temporal models with long-range dependence in applied sciences (telecommunications and econometrics) and the scaling transition arising when the number of spatial components and time scale increase at different rates.This book is intended for advanced graduate and PhD students, as well as researchers and practitioners in the fields of stochastic processes, spatial statistics, econometrics and telecommunications, although researchers working in applied sciences such as geophysics will also find value in its study.