Stable Probability Measures On Euclidean Spaces And On Locally Compact Groups
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Stable Probability Measures On Euclidean Spaces And On Locally Compact Groups
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Author : Wilfried Hazod
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Stable Probability Measures On Euclidean Spaces And On Locally Compact Groups written by Wilfried Hazod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Stable Probability Measures On Euclidean Spaces And On Locally Compact Groups
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Author : Wilfried Hazod
language : en
Publisher:
Release Date : 2014-01-15
Stable Probability Measures On Euclidean Spaces And On Locally Compact Groups written by Wilfried Hazod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Probabilities On The Heisenberg Group
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Author : Daniel Neuenschwander
language : en
Publisher: Springer
Release Date : 2006-11-14
Probabilities On The Heisenberg Group written by Daniel Neuenschwander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Characterization Of Probability Distributions On Locally Compact Abelian Groups
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Author : Gennadiy Feldman
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
Characterization Of Probability Distributions On Locally Compact Abelian Groups written by Gennadiy Feldman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.
New Directions In Locally Compact Groups
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Author : Pierre-Emmanuel Caprace
language : en
Publisher: Cambridge University Press
Release Date : 2018-02-08
New Directions In Locally Compact Groups written by Pierre-Emmanuel Caprace and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-08 with Mathematics categories.
A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.
Analysis On Infinite Dimensional Lie Groups And Algebras Proceedings Of The International Colloquium
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Author : Jean Marion
language : en
Publisher: World Scientific
Release Date : 1998-10-30
Analysis On Infinite Dimensional Lie Groups And Algebras Proceedings Of The International Colloquium written by Jean Marion and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-30 with categories.
This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.
Invariant Markov Processes Under Lie Group Actions
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Author : Ming Liao
language : en
Publisher: Springer
Release Date : 2018-06-28
Invariant Markov Processes Under Lie Group Actions written by Ming Liao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Mathematics categories.
The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
2016 Matrix Annals
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Author : Jan de Gier
language : en
Publisher: Springer
Release Date : 2018-04-10
2016 Matrix Annals written by Jan de Gier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-10 with Mathematics categories.
MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.
Limit Distributions For Sums Of Independent Random Vectors
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Author : Mark M. Meerschaert
language : en
Publisher: John Wiley & Sons
Release Date : 2001-07-11
Limit Distributions For Sums Of Independent Random Vectors written by Mark M. Meerschaert and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-11 with Mathematics categories.
A comprehensive introduction to the central limit theory-from foundations to current research This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the current level of research. In synthesizing results from nearly 200 research papers and presenting them in a self-contained form, authors Meerschaert and Scheffler have produced an accessible reference that treats the central limit theory honestly and focuses on multivariate models. For researchers, it provides an efficient and logical path through a large collection of results with many possible applications to real-world phenomena. Limit Distributions for Sums of Independent Random Vectors includes a coherent introduction to limit distributions and these other features: * A self-contained introduction to the multivariate problem * Multivariate regular variation for linear operators, real-valued functions, and Borel Measures * Multivariate limit theorems: limit distributions, central limit theorems, and related limit theorems * Real-world applications Limit Distributions for Sums of Independent Random Vectors is a comprehensive reference that provides an up-to-date survey of the state of the art in this important research area.
Proceedings Of The Fourth German Japanese Symposium Infinite Dimensional Harmonic Analysis Iv
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Author : Joachim Hilgert
language : en
Publisher: World Scientific
Release Date : 2009
Proceedings Of The Fourth German Japanese Symposium Infinite Dimensional Harmonic Analysis Iv written by Joachim Hilgert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.