On the denseness of the subset of discrete distributions in a certain set of two-dimensional distributions

Abstract

In the article [Theory of Probability & Its Applications 62(2) (2018), 216–235], a class $\mathbb{W}$ of terminal joint distributions of integrable increasing processes and their compensators was introduced. In this paper, it is shown that the discrete distributions lying in $\mathbb{W}$ form a dense subset in the set $\mathbb{W}$ for ψ-weak topology with a gauge function ψ of linear growth.

Keywords

• Increasing process
• compensator
• terminal joint distribution
• Doob–Meyer decomposition
• dense set of distributions