Probability inequality

Author: Lin Zhengyan, Bai Zhidong
Publisher:
Publish Date: 2006-07-01
Features: For researchers and educators in probability and statistics, especially those new to the field, selecting an appropriate probability inequality is crucial. Probability Inequalities is a comprehensive book that introduces fundamental probability inequalities. It collects and organizes a series of commonly used basic inequalities in probability theory and provides proofs for the majority of them. In addition to well-known inequalities, the book also provides relevant references for some of them. Introduction to Probability Inequalities: Probability inequalities are indispensable tools in the theoretical research of almost all branches of probability theory and mathematical statistics. Powerful probability inequalities often play a key role in proving many probability and statistical theorems. The purpose of Probability Inequalities is to collect and organize various basic and commonly used inequalities in probability theory. This includes inequalities related to random events, random variables, distribution functions, characteristic functions, moment inequalities, and inequalities involving dependent random variables and B-value random variables. For the majority of the listed inequalities, we provide detailed proofs. For some more complex proofs, we only outline the key ideas. For certain less fundamental content (such as dependent random variables and B-value random variables), we state the relevant definitions before listing the associated inequalities.