Abstract:
The notion of scaling transition for stationary random field (RF) on Zd was introduced and studied (2015-2019) by the author and his collaborators (Donata Puplinskaite and Vytaute Pilipauskaite). The scaling limits of RF are taken over rectangles in Zd whose sides grow as O(λγi),λ→∞ for any fixed γi >0,i=1,···,d. For d=2 a scaling transition occurs at γ0 > 0 if the scaling limits are different for γ1/γ2 > γ0 and γ1/γ2 < γ0 and do not depend on γ1,γ2 otherwise. It appears that scaling transition is a general phenomenon under long-range dependence (LRD) which occurs for various models of linear and nonlinear RFs including econometrics and telecommunications. The talk discusses some recent developments in this direction, including the structure and complete description of anisotropic scaling limits of linear LRD RFs on Z3.
Biography:
Donatas Surgailis received his Doctor of Physics and Mathematics degree in 1981 from Vilnius University. From 1987 until 2016 he was a Professor at Vilnius University, retired in 2016. He was a Visiting Professor at Case Western Reserve University (Cleveland), Michigan State University, IMPA (Rio de Janeiro), ENSAE (Paris), Lille 1 University. His main research interests are stochastic processes and random fields, long-range dependence, self-similar processes, time series, and statistical inference.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai