Counterexamples in probability theory. (Q2725942)

This book is a Russian version of a book of the same author, the first edition published in 1987 [Zbl 0629.60001] and the second one in 1997 [Zbl 0884.60001]. However, the Russian edition is not an ordinary translation from the English version. In the Russian edition new examples have been included which have been selected by the author after 1985. The book contains about 300 examples concerning basic topics in probability theory and random processes. The book is divided into four chapters. Chapter 1 deals with random events and their probabilities. Chapter 2 is devoted to random variables, their distributions and basic characteristics. Chapter 3 considers counterexamples concerning limit and three-series theorems. Chapter 4 deals with stochastic processes with sections concerning Markov and stationary processes, discrete- and continuous-time martingales.NEWLINENEWLINENEWLINEThe book is well written and suitable for advanced undergraduates. The bibliography comprises 445 references including references to personal communications with some researchers. It should be mentioned the following books on counterexamples in probability theory and mathematical statistics: \textit{J. P. Romano} and \textit{A. F. Siegel} [``Counterexamples in probability and statistics'' (1986; Zbl 0587.60001)]; \textit{G. J. Székely} [``Paradoxes in probability theory and mathematical statistics'' (1986; Zbl 0605.60002)]; \textit{G. L. Wise} and \textit{E. B. Hall} [``Counterexamples in probability and real analysis'' (1993; Zbl 0827.26001)].