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Radically Elementary Probability Theory. (AM-117), Volume 117
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Edward Nelson
Language:
English
Published/Copyright:
1988
About this book
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.
Topics
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Frontmatter
i -
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Table of contents
v -
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Preface
vii -
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Acknowledgments
ix -
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1. Random variables
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2. Algebras of random variables
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3. Stochastic processes
10 -
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4. External concepts
12 -
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5. Infinitesimals
16 -
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6. External analogues of internal notions
20 -
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7. Properties that hold almost everywhere
25 -
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8. L1 random variables 30
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9. The decomposition of a stochastic process
33 -
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10. The total variation of a process
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11. Convergence of martingales
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12. Fluctuations of martingales
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13. Discontinuities of martingales
53 -
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14. The Lindeberg condition
57 -
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15. The maximum of a martingale
61 -
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16. The law of large numbers
63 -
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17. Nearly equivalent stochastic processes
72 -
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18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Lévy-Doob-Erdös-Kac-Donsker-Prokhorov theorem
75 -
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Appendix
80 -
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Index
95
Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 2, 2016
eBook ISBN:
9781400882144
Pages and Images/Illustrations in book
Main content:
107
eBook ISBN:
9781400882144
Keywords for this book
Stochastic process; Natural number; Theorem; Random variable; Probability; Martingale (probability theory); Probability space; Probability theory; Mathematics; Almost surely; Set (mathematics); Real number; Infinitesimal; Central limit theorem; Norm (mathematics); Probability measure; Axiom; Mathematical induction; Independence (probability theory); Joint probability distribution; Algebra of random variables; Cantor's diagonal argument; Subset; Projection (linear algebra); Sequence; Elementary function; Finite set; Absolute value; Probability distribution; Transfinite number; Law of large numbers; Cartesian product; Existential quantification; Measure (mathematics); Convergence of random variables; Division by zero; Indicator function; Scientific notation; Wiener process; Idealization; Chebyshev's inequality; Variable (mathematics); Internal set theory; Predictable process; Summation; Transfer principle; Bounded function; W0; Special case; Non-standard analysis; Statistical mechanics; Abraham Robinson; Standard deviation; Estimation; Orthogonal complement; Dimension (vector space); Counterexample; Product topology; Axiomatic system; N0; Total variation; Significant figures; Without loss of generality; Path space; Family of sets; Correlation coefficient; Vector space; Subalgebra; Dimension; Linear function
Audience(s) for this book
College/higher education;Professional and scholarly;
