Radically Elementary Probability Theory

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Princeton University Press, 1987 - Mathematics - 97 pages
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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.

 

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Contents

Algebras of random variables
6
External concepts
12
External analogues of internal notions
20
The decomposition of a stochastic process
33
Convergence of martingales
41
Fluctuations of martingales
48
The Lindeberg condition
57
The law of large numbers
63
Nearly equivalent stochastic processes
72
Appendix
80
Index
95
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About the author (1987)

Fresno, CA; Professor Emeritus of Sociology; California State University, Fresno

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