Characterization of probability measures based on Q-independent generalized random fields

TL;DR

This paper extends the characterization of probability measures from independent generalized random fields to Q-independent fields, highlighting that Q-independence is a broader concept than independence.

Contribution

It introduces a new characterization of probability measures based on Q-independence in generalized random fields, expanding previous results on independence.

Findings

Q-independence generalizes independence in random fields

Characterization results are extended to Q-independent fields

Independence implies Q-independence, but not vice versa

Abstract

Prakasa Rao (Studia Sci. Math. Hungar. 11 (1976) 277-282) studied a characterization of probability distributions for linear functions of independent generalized random fields. These results are extended to Q-independent generalized random fields. It is known that independence implies Q-independence but the converse is not true.