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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Jean Bertoin 著

出 版 社：

出版时间： 2006-8-1字数：版次： 1页数： 280印刷时间： 2006/08/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780521867283包装： 精装内容简介

Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.

目录

Introduction

1 Self-similar fragmentation chains

1.1 Construction of fragmentation chains

1.1.1 Preliminaries on Markov chains

1.1.2 Branching Markov chains

1.1.3 Fragmentation chains

1.2 Genealogical structure

1.2.1 The tree of generations

1.2.2 Malthusian hypotheses and the intrinsic martingale

1.2.3 A randomly tagged branch

1.3 Extinction and formation of dust for a＜0

1.3.1 Extinction

1.3.2 Formation of dust

1.4 Some strong laws for a＞0

1.4.1 A variation of the law of large numbers

1.4.2 The homogeneous case (a=0)

1.4.3 The case a＞0

1.4.4 Another strong law via renewal theory

1.5 Additive martingales (homogeneous case a=0)

1.5.1 Convergence of additive martingales

1.5.2 Some applications

1.6 Comments

2 Random partitions

2.1 Mass-partitions

2.1.1 Partitions of a unit mass

2.1.2 Interval-partitions

2.1.3 Size-biased sampling and reordering

2.2 Random mass-partitions and Poisson measures

2.2.1 Multidimensional Dirichlet distributions

2.2.2 Some preliminaries on Poisson random measures

2.2.3 Mass-partitions induced by Poisson measures

2.2.4 Gamma subordinators and Dirichlet processes

2.2.5 Stable subordinators and Poisson-Dirichlet partitions

2.3 Exchangeable random partitions

2.3.1 Some definition

2.3.2 Kingman's theory

2.3.3 Exchangeable partition probability functions

2.4 Comments

3 Exchangeable fragmentations

3.1 Homogeneous fragmentation processes

3.1.1 Fragmentation of partitions

3.1.2 Homogeneous fragmentation as Markov processes

3.1.3 Poissonian structure

3.2 Asymptotic frequencies

3.2.1 Erosion and dislocation

3.2.2 Subordinator representation of the tagged fragment

3.2.3 Levy-Ito decomposition of the tagged fragment

3.3 Self-similar fragmentations

3.3.1 Definition and first properties

3.3.2 Changing the index of self-similarity

3.3.3 Mass-fragmentations

3.4 Comments

4 Exchangeable coalescents

4.1 Kingman's coalescent

4.1.1 Genealogy of populations in the Wright-Fisher model

4.1.2 Construction of Kingman's coalescent

4.1.3 Interval representation of Kingman's coalescent

4.2 Simultaneous and multiple coagulations

4.2.1 Coagulation of partitions

4.2.2 Exchangeable coalescents and coagulation rates

4.2.3 Poissonian construction

4.2.4 Characterization of coagulation rates

4.3 Exchangeable mass-coalescents

4.3.1 Markov property

4.3.2 Dust in exchangeable mass-coalescents

……

5 Asymptotic regimes in stochastic coalescence

References

List of symbols

Index

 

 

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