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Probability inequalities. (English) Zbl 1221.60001
Berlin: Springer; Beijing: Science Press (ISBN 978-3-642-05260-6/hbk; 978-7-03-025562-4/hbk; 978-3-642-05261-3/ebook). xi, 181 p. (2010).
Probability inequalities play a major role in many areas of research in probability and statistics. This book contains a large collection of probability inequalities. The contents of the book is as follows: Chapter 1: Elementary inequalities of probabilities of events; Chapter 2: Inequalities related to commonly used distributions; Chapter 3: Inequalities related to characteristic functions; Chapter 4: Estimates of the difference for two distribution functions; Chapter 5: Probability inequalities of random variables; Chapter 6: Bounds of probabilities in terms of moments: Chapter 7: Exponential type estimates of probabilities; Chapter 8: Moment inequalities related to one or two variables; Chapter 9: Moment estimates of (maximum of) sum of random variables; Chapter 10: Inequalities related to mixing sequences; Chapter 11: Inequalities related to associative variables; Chapter 12: Inequalities about stochastic processes and Banach space valued random variables. The authors present most of the results with proofs. The book is a useful addition and a valuable source for any researcher in probability and statistics.

MSC:
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60E15 Inequalities; stochastic orderings
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