TY - JOUR
AU1 - LEONENKO, N. N.
AU2 - OLENKO, A. Ya.
AB - Random Oper. & Stock. Equ., Vol. 1, No. 1, pp. 57-67 (1993) © VSP 1993 N. N. LEONENKO and A. Ya. OLENKO Department of Mechanics and Mathematics, Kyjiv University, 252017 Kyjiv, Ukraine Received for ROSE 15 February 1991 Abstract--Tauberian and Abelian theorems for integral transforms of Hankel type are proved. The limit theorems for spherical averages of functionals of homogeneous isotropic Gaussian random fields are considered. 1. INTRODUCTION Let Rn be an -dimensional Euclidean space, s(r) = {x G Rn: ||x|| = r} a sphere in R n , and vn(r) = {x G Rn: ||z|| < r} be a ball in R n . Let £(z), R n , be a real measurable square-mean continuous homogeneous isotropic Gaussian random field with E£(z) = 0, E£2(z) = 1, and the correlation function Bn(r) = Bn(\\x\\) = E£(0)£(z). It is known [1] that there exists a bounded nondecreasing function (), ^ 0, such that Bn(r) = 2<"- 2 > j J^(Ar)(Ar)< 2 -»>^(dA), (1) where 3v(z) is the i/th-order Bessel function of the first kind and It follows from the results of [1, 2] that = (2)2(-1> jL21(Ar)( r)2-^(dA) (2) (~3)/2 where ra(dx) is an element of Lebesgue measure
TI - Tauberian theorems for correlation functions and limit theorems for spherical averages of random fields
JF - Random Operators and Stochastic Equations
DO - 10.1515/rose.1993.1.1.57
DA - 1993-01-01
UR - https://www.deepdyve.com/lp/de-gruyter/tauberian-theorems-for-correlation-functions-and-limit-theorems-for-k8HHfSvqq0
SP - 57
EP - 68
VL - 1
IS - 1
DP - DeepDyve