An Introduction to Probability and Stochastic Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1993
|
| Schriftenreihe: | Springer Texts in Statistics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem |
| Beschreibung: | 1 Online-Ressource (XII, 205p. 19 illus) |
| ISBN: | 9781461227267 9781461276432 |
| ISSN: | 1431-875X |
| DOI: | 10.1007/978-1-4612-2726-7 |
Internformat
MARC
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Datensatz im Suchindex
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| author | Berger, Marc A. |
| author_facet | Berger, Marc A. |
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| building | Verbundindex |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781461227267 9781461276432 |
| issn | 1431-875X |
| language | English |
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| spelling | Berger, Marc A. Verfasser aut An Introduction to Probability and Stochastic Processes by Marc A. Berger New York, NY Springer New York 1993 1 Online-Ressource (XII, 205p. 19 illus) txt rdacontent c rdamedia cr rdacarrier Springer Texts in Statistics 1431-875X These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s 2\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 4\p DE-604 https://doi.org/10.1007/978-1-4612-2726-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berger, Marc A. An Introduction to Probability and Stochastic Processes Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4079013-7 (DE-588)4057630-9 (DE-588)4151278-9 |
| title | An Introduction to Probability and Stochastic Processes |
| title_auth | An Introduction to Probability and Stochastic Processes |
| title_exact_search | An Introduction to Probability and Stochastic Processes |
| title_full | An Introduction to Probability and Stochastic Processes by Marc A. Berger |
| title_fullStr | An Introduction to Probability and Stochastic Processes by Marc A. Berger |
| title_full_unstemmed | An Introduction to Probability and Stochastic Processes by Marc A. Berger |
| title_short | An Introduction to Probability and Stochastic Processes |
| title_sort | an introduction to probability and stochastic processes |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie Stochastischer Prozess Einführung |
| url | https://doi.org/10.1007/978-1-4612-2726-7 |
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