A Tauberian theorem for the fields with \(OR\) spectrum. II. (Ukrainian, English) Zbl 1150.60027

Olenko, A. Ya.

Teor. Jmovirn. Mat. Stat. 74, 81-97 (2006); translation in Theory Probab. Math. Stat. 74, 93-111 (2007).

Homogeneous isotropic random fields with \(OR\) spectrum are considered. The author proves Abelian and Tauberian theorems giving connections of local behaviour of spectral function and weighted integral functionals of random fields. Representation of weighted function in the form of Hankel transforms and functional series are presented. Some examples are proposed.
[For part I, cf. ibid. Teor. Jmovirn. Mat. Stat. 73, 120–133 (2005); translation in Theory Probab. Math. Stat. 73, 135–149 (2006; Zbl 1115.60056).]

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60G60	Random fields
60F05	Central limit and other weak theorems
62E20	Asymptotic distribution theory in statistics

Keywords:

Tauberian theorem; fields with \(OR\) spectrum; Abelian theorem; homogeneous fields; isotropic fields; spectral function; Hankel transform

Citations:

Zbl 1115.60056