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Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics.
Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.
List of contents
Elementary Inequalities of Probabilities of Events.- Inequalities Related to Commonly Used Distributions.- Inequalities Related to Characteristic Functions.- Estimates of the Difference of Two Distribution Functions.- Probability Inequalities of Random Variables.- Bounds of Probabilities in Terms of Moments.- Exponential Type Estimates of Probabilities.- Moment Inequalities Related to One or Two Variables.- Moment Estimates of (Maximum of) Sums of Random Variables.- Inequalities Related to Mixing Sequences.- Inequalities Related to Associative Variables.- Inequalities about Stochastic Processes and Banach Space Valued Random Variables.
Summary
Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics.
Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.
Report
From the reviews:
"This is a relatively short book of 181 pages organized in 12 chapters with the avowed aim of introducing beginning research workers in probability and statistics to 'frequently used' inequalities. ... I would heartily recommend this book to beginning researchers wanting to find 'frequently used' inequalities and learn some of the standard arguments." (Jon Wellner, SIAM Review, Vol. 54 (2), 2012)
"This book contains a large collection of probability inequalities. ... The authors present most of the results with proofs. The book is useful addition and a valuable source for any researcher in probability and statistics." (B. L. S. Prakasa Rao, Zentralblatt MATH, Vol. 1221, 2011)
