Tauberian theorems for random fields with an OR spectrum. I. (Ukrainian, English) Zbl 1115.60056

Olenko, A. Ya.

Teor. Jmovirn. Mat. Stat. 73, 120-133 (2005); translation in Theory Probab. Math. Stat. 73, 135-149 (2006).

Summary: We obtain Abelian and Tauberian theorems describing a relationship between the asymptotic behaviour at the origin of the spectrum of a random field and that at infinity of the integral of the random field over a sphere or a ball. We consider the case of homogeneous isotropic fields with singular spectra at the origin. The asymptotic behaviour is given in terms of OR functions.

MSC:

60G60	Random fields
62E20	Asymptotic distribution theory in statistics
40E05	Tauberian theorems
60F05	Central limit and other weak theorems
26A12	Rate of growth of functions, orders of infinity, slowly varying functions
44A15	Special integral transforms (Legendre, Hilbert, etc.)

Keywords:

Tauberian theorem; Abelian theorem; slowly varying functions; random field; homogeneous field; isotropic field; spectral function; correlation function; asymptotic behaviour; strong dependence