Can somebody better explain this than the book does?

[O'Fearraigh]

It's about GARCH(1,1) processes (mainly it's all statistics and probability).
Anyway, there is the section of a book (link below) that is confusing me:
Where does "E[ln⁡(β+αz_t^2)]" come from (on page 319, the "second" page)? My other question is why does it say that "ln⁡(β+αz_t^2) holds trivially if β > 0"? Maybe it's me, but I don't think it really make sense to say that a natural log "holds"... Isn't that wording generally reserved for logical statements?

Book:

http://www.jstor.org/stable/3532198?seq=1

 

[ronm]

I do not have access the jstor repository. So would you mind to send a copy of that paper here ron_michael70@yahoo.com?

Thanks,

 

[HallsofIvy]

I do not have access the jstor repository. So would you mind to send a copy of that paper here ron_michael70@yahoo.com?

Thanks,

Perhaps you do not know that papers on jstor are copywrited and access is restricted to those people who have payed to for the privilege or belong to organizations that have payed. In other words, what you are asking O'Fearraigh to do is illegal.