How to interpret bracket, curly bracket, and the asterisk in Probability formula?

Question

At the bottom of page #3 of this paper, it steates:

• $m_{jt}=\exp\{X_tB_j\}$
• $X_t=[X_{1t} | X_{2j}] $
• $X_{1t}=[1, x_{Djt} | X_t^*]$

May I know how should I interpret the bracket, curly bracket, and the asterisk?

Thanks in advance.

Answer 1

The curly brackets are like ordinary brackets - they are just meant as parantheses to single out the argument of the exponential.

The asterisk is defined on the top of the next page of the article.

I am not sure what the brackets and the pipe signify - it could be an inner product, maybe the covariance of the two random variables. Or it could be a conditioning of sorts. Maybe it will be clearer later in the article.

Answer 2

I agree with the previous answer. However, it should be emphasized that the notations at stake are not at all specific to probability theory.