Foundations of Constructive Probability Theory

List of contents

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.

About the author

Yuen-Kwok Chan completed a Ph.D. in Constructive mathematics with Errett Bishop before leaving academia for a career in private industry. He is now an independent researcher in Probability and its applications.

Summary

This text gives a systematic, detailed constructive theory of probability theory, in the sense of Bishop's constructive mathematics. It is accessible to beginning graduate students with no prior training in constructive mathematics or probability theory and will interest readers in either discipline, as well as those interested in the intersection.

Product details

• Authors: Yuen-Kwok Chan
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.05.2021
• EAN: 9781108835435
• ISBN: 978-1-108-83543-5
• No. of pages: 550
• Series: Encyclopedia of Mathematics and its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Mathematical Analysis, Probability & statistics, Calculus & mathematical analysis, Probability and statistics, Calculus and mathematical analysis