The Borel-Cantelli Lemma

ISBN-13: 9788132206767 / Angielski / Miękka / 2012 / 106 str.

Tapas Kumar Chandra

Opis

This book features a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All results are well illustrated by means of many interesting examples.

Recenzje

From the reviews:

"This book is devoted to the famous Borel-Cantelli lemmas, which play a very important role in probability theory, in particular in limit theorems. ... The monograph is very well written, full of illustrating examples and problems ... . At the end of each chapter there is a complete ... list of references. It is a real pleasure to read this book. This monograph may be recommended not only for researchers but also for intermediate and graduate students." (Przemyslaw Matula, Mathematical Reviews, April, 2013)

Spis treści

1. Introductory Chapter.- 2. Extensions of the First Borel-Cantelli Lemma.- 3. Variants of the Second Borel-Cantelli Lemma.- 4. A Strengthened Form of the Second Borel-Cantelli Lemma.- 5. Conditional Borel-Cantelli Lemmas.- 6. Miscellaneous Results.

O autorze

Tapas Kumar Chandra is a Professor of Statistics at the Indian Statistical Institute, Kolkata, India, since 1991. He is the author of the text books A First Course in Asymptotic Theory of Statistics and A First Course in Probability Theory. Among the problems solved by him, mention must be made of the age-old problems of finding valid Edgeworth expansions of the Likelihood Ratio Statistic and other perturbed Chi-square variables under very general conditions, and of comparing Bahadur-optimal test statistics, settling the conjecture of C. R. Rao on the optimality of score test for local alternatives and obtaining very general extensions of the Kolmogorov-Etemadi SLLN, the Marcinkiewicz-Zygmund SLLN, the well known results on the L1 and Lp convergence of the normalized sample sum and an inequality of Kolmogorov. His work is co-authored with J. K. Ghosh, R. R. Bahadur, S. Ghosal, R. Mukherjee, and others.