Radically Elementary Probability Theory. (AM-117) ( Annals of Mathematics Studies )

Publication series ：Annals of Mathematics Studies

Author： Nelson Edward  

Publisher： Princeton University Press‎

Publication year： 2016

E-ISBN: 9781400882144

P-ISBN(Paperback): 9780691084732

Subject： O211 probability (probability theory, probability theory)

Keyword： 概率论（几率论、或然率论）,数理科学和化学

Language： ENG

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Description

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Chapter

Cover

Title

Copyright

Table of contents

Preface

Acknowledgments

1. Random variables

2. Algebras of random variables

3. Stochastic processes

4. External concepts

5. Infinitesimals

6. External analogues of internal notions

7. Properties that hold almost everywhere

8. L^1 random variables

9. The decomposition of a stochastic process

10. The total variation of a process

11. Convergence of martingales

12. Fluctuations of martingales

13. Discontinuities of martingales

14. The Lindeberg condition

15. The maximum of a martingale

16. The law of large numbers

17. Nearly equivalent stochastic processes

18. The de Moivre-Laplace-Lindeberg-Feller-Wiener-Lévy-Doob-Erdös-Kac-Donsker-Prokhorov theorem

Appendix

Index

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