6.11 Consider the Matrn process restricted to the integer lattice t d, and suppose data are observed on a rectangular region of size D

6.11 Consider the Matérn process restricted to the integer lattice t ∈ ℤd, and suppose data are observed on a rectangular region of size D ⊂ ℤd of size n1 ×···× nd. The purpose of this exercise is look at the outfill asymptotics problem and in particular to show that the elements of the limiting Fisher information matrix in (6.55) are finite. There are several steps.

(a) The first step is to develop a general criterion to ensure the convergence of an infinite sum, by bounding the terms of the sum by a monotone decreasing function whose integral is finite. Thus let fk, k ∈ ℤd be a sequence of finite real numbers, and suppose the sequence can be bounded by?