Radically Elementary Probability Theory. (AM-117), Volume 117 / / Edward Nelson.
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 conven...
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1988 |
| Year of Publication: | 2016 |
| Language: | English |
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Nelson, Edward, author. aut http://id.loc.gov/vocabulary/relators/aut Radically Elementary Probability Theory. (AM-117), Volume 117 / Edward Nelson. Princeton, NJ : Princeton University Press, [2016] ©1988 1 online resource (107 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 117 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Martingales (Mathematics). Probabilities. Stochastic processes. MATHEMATICS / Probability & Statistics / General. bisacsh Abraham Robinson. Absolute value. Addition. Algebra of random variables. Almost surely. Axiom. Axiomatic system. Borel set. Bounded function. Cantor's diagonal argument. Cardinality. Cartesian product. Central limit theorem. Chebyshev's inequality. Compact space. Contradiction. Convergence of random variables. Corollary. Correlation coefficient. Counterexample. Dimension (vector space). Dimension. Division by zero. Elementary function. Estimation. Existential quantification. Family of sets. Finite set. Hyperplane. Idealization. Independence (probability theory). Indicator function. Infinitesimal. Internal set theory. Joint probability distribution. Law of large numbers. Linear function. Martingale (probability theory). Mathematical induction. Mathematician. Mathematics. Measure (mathematics). N0. Natural number. Non-standard analysis. Norm (mathematics). Orthogonal complement. Parameter. Path space. Predictable process. Probability distribution. Probability measure. Probability space. Probability theory. Probability. Product topology. Projection (linear algebra). Quadratic variation. Random variable. Real number. Requirement. Scientific notation. Sequence. Set (mathematics). Significant figures. Special case. Standard deviation. Statistical mechanics. Stochastic process. Subalgebra. Subset. Summation. Theorem. Theory. Total variation. Transfer principle. Transfinite number. Trigonometric functions. Upper and lower bounds. Variable (mathematics). Variance. Vector space. W0. Wiener process. Without loss of generality. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691084749 https://doi.org/10.1515/9781400882144 https://www.degruyter.com/isbn/9781400882144 Cover https://www.degruyter.com/document/cover/isbn/9781400882144/original |
| language |
English |
| format |
eBook |
| author |
Nelson, Edward, Nelson, Edward, |
| spellingShingle |
Nelson, Edward, Nelson, Edward, Radically Elementary Probability Theory. (AM-117), Volume 117 / Annals of Mathematics Studies ; 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 |
| author_facet |
Nelson, Edward, Nelson, Edward, |
| author_variant |
e n en e n en |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Nelson, Edward, |
| title |
Radically Elementary Probability Theory. (AM-117), Volume 117 / |
| title_full |
Radically Elementary Probability Theory. (AM-117), Volume 117 / Edward Nelson. |
| title_fullStr |
Radically Elementary Probability Theory. (AM-117), Volume 117 / Edward Nelson. |
| title_full_unstemmed |
Radically Elementary Probability Theory. (AM-117), Volume 117 / Edward Nelson. |
| title_auth |
Radically Elementary Probability Theory. (AM-117), Volume 117 / |
| title_alt |
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 |
| title_new |
Radically Elementary Probability Theory. (AM-117), Volume 117 / |
| title_sort |
radically elementary probability theory. (am-117), volume 117 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2016 |
| physical |
1 online resource (107 p.) Issued also in print. |
| 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 |
| isbn |
9781400882144 9783110494914 9783110442496 9780691084749 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA274 |
| callnumber-sort |
QA 3274.5 N45 41987EB |
| url |
https://doi.org/10.1515/9781400882144 https://www.degruyter.com/isbn/9781400882144 https://www.degruyter.com/document/cover/isbn/9781400882144/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
519 - Probabilities & applied mathematics |
| dewey-full |
519.2 |
| dewey-sort |
3519.2 |
| dewey-raw |
519.2 |
| dewey-search |
519.2 |
| doi_str_mv |
10.1515/9781400882144 |
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979911355 |
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AT nelsonedward radicallyelementaryprobabilitytheoryam117volume117 |
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n |
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cr |
| hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
| is_hierarchy_title |
Radically Elementary Probability Theory. (AM-117), Volume 117 / |
| container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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