A road to randomness in physical systems
The book is based on the author's Ph. D. dissertation, and is devoted to a unifying theory of Hopf's method of arbitrary functions given by Hopf in the 1930s and forgotten in the last period. It is shown that most applications of the Hopf method follow from the fact that the fractional part of the product of a real number \(t\) and an absolutely continuous random vector \(X\) converges to a distribution uniform on the unit hypercube as \(t\to\infty\). Therefore, the author presents new results on this convergence (Chapter 3 and 4). The Hopf method with its application is studied in Chapter 5.
scientific article; zbMATH DE number 52844