Spatial Branching Processes, Random Snakes and Partial Differential Equations
Springer Basel (Verlag)
978-3-7643-6126-6 (ISBN)
I An Overview.- I.1 Galton-Watson processes and continuous-state branching processes.- I.2 Spatial branching processes and superprocesses.- I.3 Quadratic branching and the Brownian snake.- I.4 Some connections with partial differential equations.- I.5 More general branching mechanisms.- I.6 Connections with statistical mechanics and interacting particle systems.- II Continuous-state Branching Processes and Superprocesses.- II.1 Continuous-state branching processes.- II.2 Superprocesses.- II.3 Some properties of superprocesses.- II.4 Calculations of moments.- III The Genealogy of Brownian Excursions.- III.1 The Itô excursion measure.- III.2 Binary trees.- III.3 The tree associated with an excursion.- III.4 The law of the tree associated with an excursion.- III.5 The normalized excursion and Aldous' continuum random tree.- IV The Brownian Snake and Quadratic Superprocesses.- IV.1 The Brownian snake.- IV.2 Finite-dimensional marginals of the Brownian snake.- IV.3 The connection with superprocesses.- IV.4 The case of continuous spatial motion.- IV.5 Some sample path properties.- IV.6 Integrated super-Brownian excursion.- V Exit Measures and the Nonlinear Dirichlet Problem.- V.1 The construction of the exit measure.- V.2 The Laplace functional of the exit measure.- V.3 The probabilistic solution of the nonlinear Dirichlet problem.- V.4 Moments of the exit measure.- VI Polar Sets and Solutions with Boundary Blow-up.- VI.1 Solutions with boundary blow-up.- VI.2 Polar sets.- VI.3 Wiener's test for the Brownian snake.- VI.4 Uniqueness of the solution with boundary blow-up.- VII The Probabilistic Representation of Positive Solutions.- VII.1 Singular solutions and boundary polar sets.- VII.2 Some properties of the exit measure from the unit disk.- VII.3 The representationtheorem.- VII.4 Further developments.- VIII Lévy Processes and the Genealogy of General Continuous-state Branching Processes.- VIII.1 The discrete setting.- VIII.2 Lévy processes.- VIII.3 The height process.- VIII.4 The exploration process.- VIII.5 Proof of Theorem 2.- Bibliographical Notes.
"Concise and essentially self-contained... A very accessible text...written by a leading expert of the field... It provides a clear and precise presentation of several important aspects of the theory...developed over the recent years. There is no doubt that such a monograph will be used both by beginners to learn the theory and by experts as a reference text."
-Zentralblatt Math.
Erscheint lt. Verlag | 1.7.1999 |
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Reihe/Serie | Lectures in Mathematics. ETH Zürich |
Zusatzinfo | 163 p. |
Verlagsort | Basel |
Sprache | englisch |
Gewicht | 345 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | classification • Mechanics • partial differential equation • PDE • Probability Theory • stochastics |
ISBN-10 | 3-7643-6126-3 / 3764361263 |
ISBN-13 | 978-3-7643-6126-6 / 9783764361266 |
Zustand | Neuware |
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