Asymptotic properties for partial sum processes of a Gaussian random field

Hee-Jin Moon and Yong-Kab Choi

Statistics & Probability Letters, 2007, vol. 77, issue 1, 9-18

Abstract: Let be a centered strictly stationary Gaussian random field, where is the d-dimensional lattice of all points in d-dimensional Euclidean space having nonnegative integer coordinates. Put Sn=[summation operator]0[less-than-or-equals, slant]j[less-than-or-equals, slant]n[xi]j for and [sigma]2([short parallel]i-j[short parallel])=E(Si-Sj)2 for i[not equal to]j, where [short parallel]·[short parallel] denotes the Euclidean norm and [sigma](·) is a nondecreasing continuous regularly varying function. Under some additional conditions, we investigate asymptotic properties for increments of partial sum processes of .

Keywords: Stationary; Gaussian; random; field; Regularly; varying; function; Large; deviation; probability (search for similar items in EconPapers)
Date: 2007
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