Eberhard Siebert – författare
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5 produkter
5 produkter
Del 531 - Mathematics and Its Applications
Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups
Structural Properties and Limit Theorems
Inbunden, Engelska, 2001
1 083 kr
Skickas inom 10-15 vardagar
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.
Häftad, Tyska, 2026
297 kr
Skickas inom 5-8 vardagar
E-bok
Tyska, 2026176 kr
Läs direkt efter köp
Der seit dem 19. Jahrhundert in Deutschland heimische Schüttelreim verdankt seinen Reiz und seine anhaltende Faszination der spielerischen Verschränkung von Reimanfängen und Wortbedeutungen. Trotz seiner Kürze vermag er Sachverhalte aus praktisch allen Lebensbereichen zu bewältigen – beispielsweise serviert das erste Kapitel kulinarische Spezialitäten, darunter das biblische Manna und den türkischen Döner. Aber auch den unterschiedlichsten Tonlagen und Sinnebenen wird der Schüttelreim gerecht: von poetisch bis frivol, von tiefsinnig bis banal, von unlogisch bis gänzlich unsinnig.Die Illustrationen von Ilka Birthelmer sind nicht nur eine ansprechende optische Beigabe, sondern decken auch manche vielleicht verborgene Nuance auf.
Del 531 - Mathematics and Its Applications
Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups
Structural Properties and Limit Theorems
Häftad, Engelska, 2010
1 083 kr
Skickas inom 10-15 vardagar
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.
E-bok
PDF, Engelska, 20131 367 kr
Läs direkt efter köp
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.