Foundations of Constructive Probability Theory

This book provides a systematic, detailed, and general constructive theory of probability theory and stochastic processes, with original existence and continuity theorems and results and methods previously unknown in constructive and nonconstructive settings. It is accessible to probabilists and constructive mathematicians interested in the foundations of their speciality.

Format: Hardback
Length: 550 pages
Publication date: 27 May 2021
Publisher: Cambridge University Press

This monograph presents a comprehensive and systematic constructive theory of probability theory and stochastic processes, building upon Bishop's work on constructive analysis. It offers a detailed account of this theory, including numerous original constructive existence and continuity theorems. Furthermore, it presents previously unknown results and methods in both constructive and nonconstructive settings. The text assumes a basic understanding of logic and mathematics, making it accessible to probabilists interested in the foundations of their field and constructive mathematicians seeking to apply Bishop's theory to a particular area.

The monograph begins by introducing the fundamental concepts and principles of probability theory and stochastic processes, providing a foundation for the subsequent development of the constructive theory. It then explores Bishop's constructive analysis framework, which allows for the development of rigorous and mathematical proofs of existence and continuity theorems for probability distributions and stochastic processes.

One of the key features of the monograph is its originality in the development of constructive existence and continuity theorems. Almost all of the theorems presented in the book are original, and they contribute significantly to the field of constructive probability theory. These theorems provide a powerful tool for proving the existence of solutions to various probability and stochastic problems, and they have applications in fields such as finance, insurance, and operations research.

In addition to the development of constructive existence and continuity theorems, the monograph also contains a range of results and methods that have not been previously known in the constructive and nonconstructive settings. These results and methods are based on the principles of constructive analysis and provide new insights into the behavior of probability distributions and stochastic processes.

The text is written in a clear and concise manner, making it accessible to readers with a basic understanding of logic and mathematics. It assumes no prior training in constructive mathematics or probability theory, and it provides a comprehensive introduction to the subject matter. The monograph is organized into chapters, each focusing on a specific aspect of the constructive theory of probability theory and stochastic processes.

Overall, this monograph is a valuable contribution to the field of probability theory and stochastic processes. It provides a systematic and comprehensive framework for developing constructive existence and continuity theorems, and it offers new results and methods that have not been previously known in the constructive and nonconstructive settings. The text is accessible to a wide range of readers, and it will be of interest to probabilists interested in the foundations of their speciality and constructive mathematicians who wish to see Bishop's theory applied to a particular field.

Weight: 1130g
Dimension: 163 x 242 x 46 (mm)
ISBN-13: 9781108835435