Radically Elementary Probability Theory. (AM-117), Volume 117 / Edward Nelson.

Format:

Book

Author/Creator:

Nelson, Edward, author.

Series:

Annals of mathematics studies ; no. 117.

Annals of Mathematics Studies ; 120

Language:

English

Subjects (All):

Martingales (Mathematics).

Stochastic processes.

Probabilities.

Physical Description:

1 online resource (109 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

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. L1 random variables 30

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

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882144

1400882141

OCLC:

979911355