Discrete Stochastics

Discrete stochastics is the theory of discrete probability spaces. This undergraduate textbook gives a concise introduction into discrete stochastics in general, and into a variety of typical special topics in this field, such as information theory, fluctuation theory, and semigroups of stochastic matrices. The emphasis lies on probability theory rather than on statistical methodology. Motivations, interpretations, and numerous examples and exercises relate the mathematical theory to stochastic experience. Front Matter....Pages I-X Introduction....Pages 1-18 Markovian Dynamics....Pages 19-43 Discrete Probability Spaces....Pages 45-63 Independent Identically Distributed (IID) Random Variables....Pages 65-101 Statistics....Pages 103-118 Markov Processes....Pages 119-154 Elements of Information Theory....Pages 155-183 Fluctuation Theory....Pages 185-218 Optimal Strategies in Casinoes: Red and Black....Pages 219-233 Foundational Problems....Pages 235-255 Back Matter....Pages 256-283