Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural Properties and Limit Theorems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2001
|
| Schriftenreihe: | Mathematics and Its Applications
531 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups |
| Beschreibung: | 1 Online-Ressource (XVII, 612 p) |
| ISBN: | 9789401730617 9789048158324 |
| DOI: | 10.1007/978-94-017-3061-7 |
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| 245 | 1 | 0 | |a Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups |b Structural Properties and Limit Theorems |c by Wilfried Hazod, Eberhard Siebert |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2001 | |
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| 500 | |a Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups | ||
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Datensatz im Suchindex
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-3061-7 |
| format | Electronic eBook |
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| id | DE-604.BV042424312 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401730617 9789048158324 |
| language | English |
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| series2 | Mathematics and Its Applications |
| spelling | Hazod, Wilfried Verfasser aut Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems by Wilfried Hazod, Eberhard Siebert Dordrecht Springer Netherlands 2001 1 Online-Ressource (XVII, 612 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 531 Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups Mathematics Topological Groups Harmonic analysis Functional analysis Distribution (Probability theory) Probability Theory and Stochastic Processes Topological Groups, Lie Groups Abstract Harmonic Analysis Measure and Integration Functional Analysis Mathematik Siebert, Eberhard Sonstige oth https://doi.org/10.1007/978-94-017-3061-7 Verlag Volltext |
| spellingShingle | Hazod, Wilfried Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems Mathematics Topological Groups Harmonic analysis Functional analysis Distribution (Probability theory) Probability Theory and Stochastic Processes Topological Groups, Lie Groups Abstract Harmonic Analysis Measure and Integration Functional Analysis Mathematik |
| title | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems |
| title_auth | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems |
| title_exact_search | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems |
| title_full | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems by Wilfried Hazod, Eberhard Siebert |
| title_fullStr | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems by Wilfried Hazod, Eberhard Siebert |
| title_full_unstemmed | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups Structural Properties and Limit Theorems by Wilfried Hazod, Eberhard Siebert |
| title_short | Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups |
| title_sort | stable probability measures on euclidean spaces and on locally compact groups structural properties and limit theorems |
| title_sub | Structural Properties and Limit Theorems |
| topic | Mathematics Topological Groups Harmonic analysis Functional analysis Distribution (Probability theory) Probability Theory and Stochastic Processes Topological Groups, Lie Groups Abstract Harmonic Analysis Measure and Integration Functional Analysis Mathematik |
| topic_facet | Mathematics Topological Groups Harmonic analysis Functional analysis Distribution (Probability theory) Probability Theory and Stochastic Processes Topological Groups, Lie Groups Abstract Harmonic Analysis Measure and Integration Functional Analysis Mathematik |
| url | https://doi.org/10.1007/978-94-017-3061-7 |
| work_keys_str_mv | AT hazodwilfried stableprobabilitymeasuresoneuclideanspacesandonlocallycompactgroupsstructuralpropertiesandlimittheorems AT sieberteberhard stableprobabilitymeasuresoneuclideanspacesandonlocallycompactgroupsstructuralpropertiesandlimittheorems |