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Radically Elementary Probability Theory. (AM-117), Volume 117 : Annals of Mathematics Studies - Edward Nelson

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

Annals of Mathematics Studies

Paperback Published: 1st September 1987
ISBN: 9780691084749
Number Of Pages: 107

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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.

Frontmatter, pg. iTable of contents, pg. vPreface, pg. viiAcknowledgments, pg. ix1. Random variables, pg. 12. Algebras of random variables, pg. 63. Stochastic processes, pg. 104. External concepts, pg. 125. Infinitesimals, pg. 166. External analogues of internal notions, pg. 207. Properties that hold almost everywhere, pg. 258. L1 random variables 30, pg. 309. The decomposition of a stochastic process, pg. 3310. The total variation of a process, pg. 3711. Convergence of martingales, pg. 4112. Fluctuations of martingales, pg. 4813. Discontinuities of martingales, pg. 5314. The Lindeberg condition, pg. 5715. The maximum of a martingale, pg. 6116. The law of large numbers, pg. 6317. Nearly equivalent stochastic processes, pg. 7218. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Levy-Doob-Erdos-Kac-Donsker-Prokhorov theorem, pg. 75Appendix, pg. 80Index, pg. 95

ISBN: 9780691084749
ISBN-10: 0691084742
Series: Annals of Mathematics Studies : Book 117
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 107
Published: 1st September 1987
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 16.51  x 0.64
Weight (kg): 0.16

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