Spatial branching processes, random snakes, and partial differential equations

✍ Scribed by Le Gall, Jean-François

Publisher: Birkhäuser
Year: 1999
Tongue: English
Leaves: 169
Series: Lectures in mathematics ETH Zürich
Edition: 1999
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations (PDE). The Brownian snake approach is used to give a powerful representation of superprocesses and also to investigate connections between superprocesses and PDEs. These are notable because almost every important probabilistic question corresponds to a significant analytic problem

✦ Table of Contents

Front Matter....Pages i-ix
An Overview....Pages 1-20
Continuous-state Branching Processes and Superprocesses....Pages 21-40
The Genealogy of Brownian Excursions....Pages 41-51
The Brownian Snake and Quadratic Superprocesses....Pages 53-74
Exit Measures and the Nonlinear Dirichlet Problem....Pages 75-88
Polar Sets and Solutions with Boundary Blow-up....Pages 89-109
The Probabilistic Representation of Positive Solutions....Pages 111-128
Lévy Processes and the Genealogy of General Continuous-state Branching Processes....Pages 129-149
Back Matter....Pages 151-163

✦ Subjects

Mathematics, general

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