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Can anyone suggest me some good reference books on Asymptotic Theory of Statistics and Probability for students pursuing a post-graduate degree in Statistics ?

It would be very much helpful if the stated reference book(s) contained enough solved problems on the afore-mentioned topic, so as to get a good hold on the topic.

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As for probability, I would recommend: Borovkov, Probability theory http://www.springer.com/us/book/9781447152002 It seems to be the only textbook that contains Stone's local limit theorems.

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    $\begingroup$ Sir, I specifically (and desperately.... to a great extent) require a book on Asymptotic theory of Statistics... the Statistics part is needed more than the Probability part.... :-( $\endgroup$
    – Dwaipayan Gupta
    Commented May 30, 2016 at 17:08
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    $\begingroup$ There is a book by the same author crcpress.com/Mathematical-Statistics/Borokov/p/book/… , but the price is unreasonable. This book is more devoted to fundamentals of mathematical statistics than to applications. $\endgroup$
    – Viktor
    Commented May 30, 2016 at 17:18

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