Sums of Independent Random Variables (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 82) by V.V. Petrov (PDF)

Description

The classic “Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari­ ables” by B. V. Gnedenko and A. N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel­ oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I. A. Ibragi­ mov and Yu. V. I~innik, “Independent and Stationarily Connected VaTiables”, which appeared in 1965, contains an exposition of the contem­ porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri­ buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I really appreciate this book. So far I am half way through but I wanted to write a review before finishing because this book makes everything a lot easier. Theorems are given in such an integrated way that you dont get stuck and spend a lot of time to understand the preliminaries. Very clear and complete. You can benefit a lot if you are studying convergence of random variable. Thanks Petrov.

⭐It’s an excellent book for PhD students working on convergence theorem in stochastic simulation.

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