When studying complex phenomena which are both dynamic and random, we need the theory of stochastic processes. In this area, Gaussian processes (GPs) play a fundamental role similar to the well-known role played by the normal distribution in classical and modern probability and statistics. Thousands of articles and lots of books on GPs are available in the literature. If, e.g., a young scientist at a PhD level wants to study elements of modern GPs, she/he will, most likely, be in trouble. This is because there are too many books, most of them of huge size and covering an enormous variety of topics.
The book under review can be recommended to this group of potential readers and definitely to a wider audience of pure and applied mathematicians.
The book contains well selected topics, well explained basic notions, a reasonable number of basic results which are clearly formulated and followed by proofs and illustrative examples. Among the topics which are covered by this book are Gaussian processes and measures, white noise, the Cameron-Martin theorem, isoperimetric inequalities, the concentration principle and measure concavity, the large deviations principle, the functional law of the iterated logarithm, small deviations and the entropy method, expansions of Gaussian elements, the quantization of Gaussian vectors.
It seems a little surprising, but all these topics are covered in 120 pages, including references and index. This interestingly designed and reasonably priced softcover book appears in the series Springer Briefs in Mathematics. Once again, the book is highly recommended!