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This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems.

While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

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Definitions and preliminary facts.- The method of convolutions.- Local lattice estimates.- Uniform lattice estimates.- Total variation of lattice measures.- Non-uniform estimates for lattice measures.- Discrete non-lattice approximations.- Absolutely continuous approximations.- The Esseen type estimates.- Lower estimates.- The Stein method.- The triangle function method.- Heinrich´s method for m-dependent variables.- Other methods.- Solutions to selected problems.- Bibliography.- Index.

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"This book is designed for a Ph.D. level graduate course focusing on the various methods that can be employed to measure the accuracy of probability model approximations. ... laid out clearly, with very valuable bibliographical notes and detailed references at the end of each topic. Each chapter concludes with a set of problems. ... An additional study aid is the inclusion of boxed summaries giving typical applications for the given technique along with the advantages and drawbacks of the method." (N. C. Weber, Mathematical Reviews, 2017)

"This book is an excellent starting point for those new to the area, and a useful reference for more experienced researchers. It brings together a wide range of techniques for probabilistic approximations in a way which is accessible to a reader with a modest background in probability. The presentation is user-friendly, giving the reader all that is needed to select and apply appropriate methods for a range of approximation problems." (Fraser Daly, zbMATH 1345.60005, 2016)

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Vydas Cekanavicius is Professor of Statistics at Vilnius University. In 2005, he was co-winner of the Lithuanian State Award of Science for his research on compound approximations in probability theory. In his native country Lithuania, he is best known as the co-author of a best-selling three-volume textbook on statistics.

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