Some remarks on scaling transition in limit theorems for random fields

2019/03/22 by Julius Damarackas, Damarackas, Julius, Vygantas Paulauskas +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G60 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.09399

openalex publication_date 2019/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we present simple examples of linear random fields defined on \ZZ² and \ZZ³ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand the mechanism of appearance of this phenomenon better. In previous papers devoted to the scaling transition it was proved mainly for random fields with finite variance and long-range dependence. We consider random fields with finite and infinite variance. Our examples show that the scaling transition phenomenon can be observed for linear random fields with the so-called negative dependence, which is part of short-range dependence. Relation of the scaling transition with Lamperti type theorems for random fields is discussed.

Related

• Scaling transition for long-range dependent Gaussian random fields
• Scaling transition and edge effects for negatively dependent linear random fields on ℤ²
• Scaling transition for singular linear random fields on ℤ²: spectral approach
• Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates
• Invariance principles for operator-scaling Gaussian random fields