Asymptotic Behaviour of Linearly Transformed Sums of Random Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
416 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently |
| Beschreibung: | 1 Online-Ressource (XV, 504 p) |
| ISBN: | 9789401155687 9789401063463 |
| DOI: | 10.1007/978-94-011-5568-7 |
Internformat
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| 500 | |a Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently | ||
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Datensatz im Suchindex
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| bvnumber | BV042423988 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-5568-7 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789401155687 9789401063463 |
| language | English |
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| spelling | Buldygin, Valery Verfasser aut Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by Valery Buldygin, Serguei Solntsev Dordrecht Springer Netherlands 1997 1 Online-Ressource (XV, 504 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 416 Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently Mathematics Sequences (Mathematics) Systems theory Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Sequences, Series, Summability Measure and Integration Systems Theory, Control Mathematik Statistik Asymptotik (DE-588)4126634-1 gnd rswk-swf Zufallsvektor (DE-588)4191098-9 gnd rswk-swf Reihe (DE-588)4049197-3 gnd rswk-swf Zufallsvektor (DE-588)4191098-9 s Reihe (DE-588)4049197-3 s Asymptotik (DE-588)4126634-1 s 1\p DE-604 Solntsev, Serguei Sonstige oth https://doi.org/10.1007/978-94-011-5568-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buldygin, Valery Asymptotic Behaviour of Linearly Transformed Sums of Random Variables Mathematics Sequences (Mathematics) Systems theory Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Sequences, Series, Summability Measure and Integration Systems Theory, Control Mathematik Statistik Asymptotik (DE-588)4126634-1 gnd Zufallsvektor (DE-588)4191098-9 gnd Reihe (DE-588)4049197-3 gnd |
| subject_GND | (DE-588)4126634-1 (DE-588)4191098-9 (DE-588)4049197-3 |
| title | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables |
| title_auth | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables |
| title_exact_search | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables |
| title_full | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by Valery Buldygin, Serguei Solntsev |
| title_fullStr | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by Valery Buldygin, Serguei Solntsev |
| title_full_unstemmed | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by Valery Buldygin, Serguei Solntsev |
| title_short | Asymptotic Behaviour of Linearly Transformed Sums of Random Variables |
| title_sort | asymptotic behaviour of linearly transformed sums of random variables |
| topic | Mathematics Sequences (Mathematics) Systems theory Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Sequences, Series, Summability Measure and Integration Systems Theory, Control Mathematik Statistik Asymptotik (DE-588)4126634-1 gnd Zufallsvektor (DE-588)4191098-9 gnd Reihe (DE-588)4049197-3 gnd |
| topic_facet | Mathematics Sequences (Mathematics) Systems theory Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Sequences, Series, Summability Measure and Integration Systems Theory, Control Mathematik Statistik Asymptotik Zufallsvektor Reihe |
| url | https://doi.org/10.1007/978-94-011-5568-7 |
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