Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY, called the product convolution of F and G.

We consider a space-time random field on ℝd × ℝ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and ...