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?

  • $\begingroup$ 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

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."

  • 1
    $\begingroup$ 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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