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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?

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  • $\begingroup$ It all depends on how rigorous you would like to be. Serious asymptotic analysis requires knowledge of measure theory. $\endgroup$ – JohnK Jul 14 '17 at 16:48
  • $\begingroup$ I am working on a physics problem and right now some part of it become a complex probability theory problem where I have defined a quantity which is sum of large number of dependent random variables where each variable is linear transformed form of binomial random variable. I realize that, sooner or later I will have to do some serious mathematical calculations which will be some variant of some general form of 'central limit theorem'. Hence I thing, my level of interest in asymptotic analysis will be of moderate level, not too abstract mathematical and also not too easy. $\endgroup$ – aranyak Jul 14 '17 at 17:02
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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."

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    $\begingroup$ Isn't this book about asymptotic expansions (of sequences, functions, power series, you name it) using $o,O$ notations ? I don't remember seeing anything probabilistic in there. $\endgroup$ – Gabriel Romon Nov 9 '17 at 15:00

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