Foundations of Constructive Probability Theory

This book provides a systematic and general theory of probability within the framework of constructive mathematics.

Yuen-Kwok Chan (Author)

9781108835435, Cambridge University Press

Hardback, published 27 May 2021

550 pages
15 x 23 x 4 cm, 1.12 kg

'This book is an important contribution to Bishop-style constructive mathematics (BISH), as it offers an elaborate development of constructive probability theory within Bishop-Cheng Measure Theory (BCMT).' Iosif Petrakis, zbMATH

Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

Part I. Introduction and Preliminaries: 1. Introduction
2. Preliminaries
3. Partition of unity
Part II. Probability Theory: 4. Integration and measure
5. Probability space
Part III. Stochastic Process: 6. Random field and stochastic process
7. Measurable random field
8. Martingale
9. a.u. continuous process
10. a.u. càdlàg process
11. Markov process
Appendix A. Inverse function theorem
Appendix B. Change of integration variables
Appendix C. Taylor's theorem
References
Index.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK]