Author | Gall, Jean-Franรงois Le. author |
---|---|
Title | Spatial Branching Processes, Random Snakes and Partial Differential Equations [electronic resource] / by Jean-Franรงois Le Gall |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8683-3 |
Descript | 163 p. online resource |
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 Itรด 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 Aldousโ 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 Wienerโs 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 representation theorem -- VII.4 Further developments -- VIII Lรฉvy Processes and the Genealogy of General Continuous-state Branching Processes -- VIII.1 The discrete setting -- VIII.2 Lรฉvy processes -- VIII.3 The height process -- VIII.4 The exploration process -- VIII.5 Proof of Theorem 2 -- Bibliographical Notes