Originally Posted by

**Volga** The text I am reading uses some notation that I am not sure about. The only other place I saw that was in denoting limit from the left/right. Here I am not sure whether it means the same or something else.

quoting

The Central Limit Theorem (Bingham and Kiesel Section 2.9) tells us that

$\displaystyle Pr_Q[M_T\leq-d_+]->\Phi(-d_+)=1-\Phi(d_+)$

ie

$\displaystyle Pr_Q[M_T\geq-d_+]->\Phi(d_+)$

and similarly

$\displaystyle Pr_Q[M_T\geq-d_-]->\Phi(d_-)$

end quote

I don't have the above textbook and I've seen more than one version of Central Limit Theorem. So, my questions,

(1) is the above simply saying that the distribution of $\displaystyle M_T$ converges to N(0,1)?

(2) is the notation $\displaystyle d_+$ etc is to denote right/left continuity?

thanks