Introduction to random times and quantum randomness. (English) Zbl 1021.81500

Amadora: McGraw-Hill. 188 p. (2001).
This book of which the title is somewhat misleading in the sense that it is to understand as random instants and quantum randomness is a pedagogical introduction to the role of probability in random walks and Markov chains on the one hand, and quantum mechanics on the other hand. On the surface, one of the main goals of this monography is to put in evidence the differences and the similarities of these two concepts of probability and to this end, the text is split into two parts, Part 1, which deals with random instants, and Part 2, which examines quantum randomness in a detailed manner. The main topics covered are random walks and stopping instants, martingales, discrete and continuous Markov chains, von Neumann quantum mechanics and Feyman quantum mechanics.
This book is written for (young) mathematicians, a student in physics may have some difficulty to read it. For instance von Neumann’s axioms could have been introduced in a simpler manner, and the use of probabilistic tribe could be deleted.


81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81Sxx General quantum mechanics and problems of quantization
60H30 Applications of stochastic analysis (to PDEs, etc.)