Decision Systems and Nonstochastic Randomness

"Decision Systems and Non-stochastic Randomness" is the first systematic presentation and mathematical formalization (including existence theorems) of the statistical regularities of non-stochastic randomness. The results presented in this book extend the capabilities of probability theory by providing mathematical techniques that allow for the description of uncertain events that do not fit standard stochastic models. The book demonstrates how non-stochastic regularities can be incorporated into decision theory and information theory, offering an alternative to the subjective probability approach to uncertainty and the unified approach to the measurement of information. This book is intended for statisticians, mathematicians, engineers, economists or other researchers interested in non-stochastic modeling and decision theory.

“Decision Systems and Nonstochastic Randomness” presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. Each self-contained chapter of this neatly-structured monograph includes a detailed introduction and summary of its contents. The included results are presented not only with rigorous proofs but also through numerous intuitive examples. An appendix is provided which includes classic results from the theory of functions and measured sets as well as decision theory, offering an overview of the necessary prerequisites. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines. Because of these far-reaching implications, this book may be a useful resource for statisticians, mathematicians, engineers, economists and other utilizing nonstochastic modeling and decision theory.