Measure-Valued Branching Markov Processes

✍ Scribed by Zenghu Li (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 355
• Series: Probability and Its Applications
• Edition: 1
• Category: Library

✦ Synopsis

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups.

The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

✦ Table of Contents

Front Matter....Pages I-XI
Random Measures on Metric Spaces....Pages 1-28
Measure-Valued Branching Processes....Pages 29-56
One-Dimensional Branching Processes....Pages 57-85
Branching Particle Systems....Pages 87-105
Basic Regularities of Superprocesses....Pages 107-125
Constructions by Transformations....Pages 127-144
Martingale Problems of Superprocesses....Pages 145-178
Entrance Laws and Excursion Laws....Pages 179-206
Structures of Independent Immigration....Pages 207-232
State-Dependent Immigration Structures....Pages 233-253
Generalized Ornstein–Uhlenbeck Processes....Pages 255-280
Small-Branching Fluctuation Limits....Pages 281-299
Back Matter....Pages 301-350

✦ Subjects

Probability Theory and Stochastic Processes