Q:

Reference: Asymptotic analysis in probability theory

I am from physics background. I want to learn "limit theorems in probability theory". So recently I started reading some books. But I realize a need to get used to with asymptotic analysis. I know that asymptotic analysis in huge field and I don't want to learn everything. I want to get skillful in only small part of asymptotic analysis which will be helpful in realizing probability limit theorems.
So the question is, What are the references (books, online-notes, etc.) for that? 

A:

Have you heard of Asymptotic Methods in Analysis by De Bruijn? From the preface:

"[The book's] purpose is to teach asymptotic methods by explaining a number of examples in every detail, so as to suit beginners who seriously want to acquire some technique in attacking asymptotic problems."
[...]
"This book has not been written exclusively for mathematicians, but also for those physicists and engineers who have a certain maturity with respect to analysis, including some general knowledge of complex function theory."

