Sentence examples for acceptable random from inspiring English sources

In this paper, we combine the concept of conditioning on a σ-algebra with the concept of acceptability (in fact, wide acceptability) and define conditionally acceptable random variables.

It is clear that acceptable random variables are extended acceptable.

The following example constructed by Wang et al. [10] can illustrate that widely acceptable random variables properly include acceptable random variables.

If {X n, n ≥ 1} is a sequence of acceptable random variables, then {-X n, n ≥ 1} is still a sequence of acceptable random variables.

Problem 1.3 For much weaker random variables than acceptable random variables, we wonder whether there are also some results similar to that of acceptable random variables.

In the following, we will provide the Hoeffding-type inequality for acceptable random variables.

Furthermore, we will study the complete convergence for acceptable random variables using the exponential inequalities.

Firstly, we will recall the definitions of negatively orthant dependent random variables and acceptable random variables.

Studying the limiting behavior of acceptable random variables is of interest.

We will study the complete convergence for a sequence of acceptable random variables under condition (3.4).

Let {X n, n ≥ 1} be a sequence of acceptable random variables.