Random Oper, & Stock. Eqs., Vol. 1, No. 3, pp. 213-222 (1993) © VSP 1993 A. H. EL-BASSIOUNY Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt Received for ROSE 15 September 1991 Abstract--The asymptotic distributions for the functionals and are studied, where v(ri) and v(rz) are two concentric balls in R n with radii and 2 ( < 2), | · | is the Lebesgue measure, a: R n --»· R1 is a non-random continuous radial function and () is a homogeneous isotropic Gaussian random field such that the integral of the correlation function diverges. 1. INTRODUCTION In this article we consider limit distributions of functionals which are measures of random formations between two concentric cylinders, generated by the intersection of a random field with certain radial function. Our main attention is drawn to Gaussian random fields such that the integral of the correlation function diverges. Problems involving sojourns of stationary Gaussian processes with a long range dependence have been studied by Herman  and Maejima . 2. MAIN RESULTS Assume that v(ri) and ^) are two concentric balls in the -dimensional Euclidean space R n with radii and TI (r\ < r^), i.e. v(r)=
Random Operators and Stochastic Equations – de Gruyter
Published: Jan 1, 1993
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