Zhengyan Lin - Böcker

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.

Probability theory is a discipline that studies the quantitative regularity of random phenomena. The fact that random phenomena arise, especially in the era of big data and artificial intelligence, determines the importance of this discipline. This volume introduces various concepts that quantitatively describe random phenomena, including probability, random variables, distribution functions, density functions, mathematical expectations, variances, moments, and characteristic functions. It finishes off by presenting probability limit theory, including various convergences.Throughout the volume, great importance is attached to the elaboration of probability thoughts. For this reason, some practical examples to illustrate the introduced concept are always used. In order to meet the needs of different levels of readers, there is a section on Supplements and Notes at the end of each chapter to enhance and expand the content in the body of the textbook. This volume contains a large number of problems of varying levels for the reader with the purpose to review, consolidate, deepen and expand their knowledge.As the only branch of mathematics that studies the quantitative regularity of random phenomena, probability theory has not only theoretical significance, but it is also a main theoretical basis of mathematical statistics. Therefore, it will be of interest to scholars from other disciplines related to random phenomena.