On the asymptotic behavior of functionals of random fields

Abstract:

The talk is about the asymptotic behavior of functionals of random fields with possible long-range dependence. New properties of generalized Hermite-type processes, the Strong Law of Large Numbers (SLLN) for random fields, and the asymptotic behavior of running maxima of random double arrays will be discussed.

New properties of generalized Hermite-type processes that arise in NLT for integral functionals of long-range dependent random

fields will be demonstrated. Contrary to the classical one-dimensional case, it will be shown that for any choice of a multidimensional observation window the generalized Hermite-type process has non-stationary increments.

The SLLN for integral functionals of random fields with unboundedly increasing covariances will be presented. The SLLN is derived for the case of increasing domains. Conditions on covariance functions such that the SLLN holds will be provided. The considered scenarios include non-stationary random fields. The discussion about applications to weak and long-range dependent random fields and numerical examples will be shown.

Results on the asymptotic behavior of running maxima functionals of random double arrays of phi-subgaussian random variables will be demonstrated. The main results are specified for various important particular scenarios and classes of phi-subgaussian random variables.