Radically Elementary Probability Theory. (AM-117), Volume 117
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. Les mer
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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.
- FAKTA
-
Utgitt:
1987
Forlag: Princeton University Press
Innbinding: Paperback
Språk: Engelsk
Sider: 107
ISBN: 9780691084749
Format: 24 x 15 cm
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*Frontmatter, pg. i*Table of contents, pg. v*Preface, pg. vii*Acknowledgments, pg. ix*1. Random variables, pg. 1*2. Algebras
of random variables, pg. 6*3. Stochastic processes, pg. 10*4. External concepts, pg. 12*5. Infinitesimals, pg. 16*6. External
analogues of internal notions, pg. 20*7. Properties that hold almost everywhere, pg. 25*8. L1 random variables 30, pg. 30*9.
The decomposition of a stochastic process, pg. 33*10. The total variation of a process, pg. 37*11. Convergence of martingales,
pg. 41*12. Fluctuations of martingales, pg. 48*13. Discontinuities of martingales, pg. 53*14. The Lindeberg condition, pg.
57*15. The maximum of a martingale, pg. 61*16. The law of large numbers, pg. 63*17. Nearly equivalent stochastic processes,
pg. 72*18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Levy-Doob-Erdos-Kac-Donsker-Prokhorov theorem, pg. 75*Appendix,
pg. 80*Index, pg. 95