\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2012f.01084}
\itemau{Boffetta, Guido; Vulpiani, Angelo}
\itemti{Probability in physics. An introduction. (Probabilit\`a in fisica. Un'introduzione.)}
\itemso{Unitext -- Collana di Fisica e Astronomia. Milano: Springer (ISBN 978-88-470-2429-8/pbk; 978-88-470-2430-4/ebook). xii, 232~p. EUR~27.84/net; SFR~37.50; \sterling~25.99; \$~39.95 (2012).}
\itemab
This book offers an overview on a large range of topics starting from some basic ideas on the definition of probability and its axiomatic construction. Much material is given in the appendix where distribution functions, mean values and some important distributions are provided. Therefore, generating functions (with application to the branching Galton-Watson model) are presented just after the notions of conditional probability and Bayes's theorem. Some basic facts about limit laws of probability like central limit, law of large numbers and some applications are dealt with in Section 3 in an intuitive approach. A short chapter is devoted to Brownian motion with historical remarks and also its interplay with symmetric random walks is mentioned. With an analogous heuristic philosophy, Markov chains and the derivation of the equation of the probability generating function for death processes is taken into account. More space is devoted to diffusion processes (a remark is given also to the stochastic integral with respect to Brownian motion and the It\^o formula). Some applications are described (for example stochastic models for climate). Some classical questions are also treated in Section 8.2 where the notion of infinitely divisible laws and the idea of stable laws are described. The book is clearly suitable for those who want to grasp basic ideas of probability without being bogged down in the measure-theoretical background. Interesting flashes of applications in mechanical statistics are provided all along the book.
\itemrv{Enzo Orsingher (Roma)}
\itemcc{U25 K55 K65 M55}
\itemut{}
\itemli{doi:10.1007/978-88-470-2430-4}
\end