Pitman / Berkeley / CA Combinatorial Stochastic Processes

1. Auflage 2006
ISBN: 978-3-540-34266-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 257 Seiten

Probability Theory and Stochastic Processes - Short description currently not available.

Autoren/Hrsg.

Pitman, Jim

Berkeley,

CA,

USA,

Inhaltsverzeichnis

1;Foreword;5
2;Contents;6
3;0 Preliminaries;9
3.1;Preface;9
3.2;Introduction;10
3.3;Brownian motion and related processes;11
3.4;Subordinators;17
4;1 Bell polynomials and Gibbs partitions;20
4.1;Notation;21
4.2;Partitions and compositions;21
4.3;Moments and cumulants;27
4.4;Random sums;30
4.5;Gibbs partitions;31
5;2 Exchangeable random partitions;43
5.1;Finite partitions;44
5.2;Infinite partitions;48
5.3;Structural distributions;52
5.4;Convergence;54
5.5;Limits of Gibbs partitions;56
6;3 Sequential constructions of random partitions;60
6.1;The Chinese restaurant process;61
6.2;The two-parameter model;65
6.3;Asymptotics;72
6.4;A branching process construction;77
7;4 Poisson constructions of random partitions;81
7.1;Size-biased sampling;82
7.2;Poisson representation of the two-parameter model;85
7.3;Representation of infinite Gibbs partitions;89
7.4;Lengths of stable excursions;91
7.5;Brownian excursions;94
8;5 Coagulation and fragmentation processes;100
8.1;Coalescents;101
8.2;Fragmentations;109
8.3;Representations of infinite partitions;112
8.4;Coagulation and subordination;115
8.5;Coagulation -- fragmentation duality;119
9;6 Random walks and random forests;124
9.1;Cyclic shifts and Lagrange inversion;125
9.2;Galton-Watson forests;128
9.3;Brownian asymptotics for conditioned Galton-Watson trees;132
9.4;Critical random graphs;138
10;7 The Brownian forest;145
10.1;Plane trees with edge-lengths;146
10.2;Binary Galton-Watson trees;148
10.3;Trees in continuous paths;151
10.4;Brownian trees and excursions;154
10.5;Plane forests with edge-lengths;164
10.6;Sampling at downcrossing times;167
10.7;Sampling at Poisson times;169
10.8;Path decompositions;174
10.9;Further developments;176
11;8 Brownian local times;178
11.1;Stopping at an inverse local time;178
11.2;Squares of Bessel processes;180
11.3;Stopping at fixed times;183
11.4;Time-changed local time processes;186
11.5;Branching process approximations;188
12;9 Brownian bridge asymptotics;193
12.1;Basins and trees;194
12.2;Mapping walks;198
12.3;Brownian asymptotics;199
12.4;The diameter;203
12.5;The height profile;205
12.6;Non-uniform random mappings;206
13;10 Random forests and the additive coalescent;207
13.1;Random p-forests and Cayley's multinomial expansion;208
13.2;The additive coalescent;210
13.3;The standard additive coalescent;213
13.4;Poisson cutting of the Brownian tree;215
14;Bibliography;221
15;Index;221
16;List of participants;221
17;List of short lectures;221