Stochastics. Theory and applications.
The book provides a well-written introduction to probability theory and statistics. It is written in German. In the first part the foundations of measure theory and the Lebesgue integral are introduced. The second part deals with elementary probability theory, i.e. probability spaces, random variables, independence, sequences and series of independent random variables, the central limit theorem, and conditional expectations. Part 3 is devoted to stochastic processes, namely Markov chains, Poisson processes , martingales in discrete time, Brownian motion, martingales in continuous time, and the Itô integral. Part 4 gives an introduction to statistics, that is estimation theory, hypothesis testing, and linear models.
scientific article; zbMATH DE number 2104347