A scalar-valued infinitely divisible random field with Polya autocorrelation

作者：Finlay Richard^*; Seneta Eugene

来源：Statistics & Probability Letters, 2017, 122: 141-146.

DOI：10.1016/j.spl.2016.11.006

• Random field
• Infinitely divisible
• Polya correlation

We construct and characterize a stationary scalar-valued random field with domain R-d or Z(d), d is an element of Z(+), which is infinitely divisible, can take any (univariate) infinitely divisible distribution with finite variance at any single point of its domain, and has autocorrelation function between any two points in its domain expressed as a product of arbitrary positive and convex functions equal to 1 at the origin. Our method of construction-based on carefully chosen sums of independent and identically distributed random variables-is simple and so lends itself to simulation.

• 出版日期2017-3