$K$-differenced vector random fields

A thin-tailed vector random field, referred to as a $K$-differenced vector random field, is introduced. Its finite-dimensional densities are the differences of two Bessel functions of second order, whenever they exist, and its finite-dimensional characteristic functions have simple closed forms as the differences of two power functions or logarithm functions. Its finite-dimensional distributions have thin tails, even thinner than those of a Gaussian one, and it reduces to a Linnik or Laplace vector random field in a limiting case. As one of its most valuable properties, a $K$-differenced vector random field is characterized by its mean and covariance matrix functions just like a Gaussian one. Some covariance matrix structures are constructed in this paper for not only the $K$-differenced vector random field, but also for other second-order elliptically contoured vector random fields. Properties of the multivariate $K$-differenced distribution are also studied.