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Spatial branching in random environments and with interaction /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, New Jersey :
World Scientific,
[2014]
|
| Colección: | Advanced series on statistical science & applied probability ;
vol. 20. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""1.7.4 The Ornstein-Uhlenbeck process""""1.7.5 Transition measures and h-transform""; ""1.8 Ito-integral and SDE�s""; ""1.8.1 The Bessel process and a large deviation result for Brownian motion""; ""1.9 Martingale change of measure""; ""1.9.1 Changes of measures, density process, uniform integrability""; ""1.9.2 Two particular changes of measures: Girsanov and Poisson""; ""1.10 The generalized principal eigenvalue for a second order elliptic operator""; ""1.10.1 Smooth bounded domains""; ""1.10.2 Probabilistic representation of λc""; ""1.11 Some more criticality theory""
- ""Contents""; ""Preface""; ""1. Preliminaries: Diffusion, spatial branching and Poissonian obstacles""; ""1.1 Notation, terminology""; ""1.2 A bit of measure theory""; ""1.3 Gronwall�s inequality""; ""1.4 Markov processes""; ""1.5 Martingales""; ""1.5.1 Basics""; ""1.5.2 Estimates for the absolute moments""; ""1.6 Brownian motion""; ""1.6.1 The measure theoretic approach""; ""1.6.2 Levy�s approach""; ""1.6.3 Some more properties of Brownian motion""; ""1.7 Diffusion""; ""1.7.1 Martingale problem, L-diffusion""; ""1.7.2 Connection to PDE�s; semigroups""; ""1.7.3 Further properties""
- ""1.12 Poissonian obstacles""""1.12.1 Wiener-sausage and obstacles""; ""1.12.2 �Annealed� and �quenched�; �soft� and �hard�""; ""1.13 Branching""; ""1.13.1 The critical case; Kolmogorov�s result""; ""1.13.2 The supercritical case; Kesten-Stigum Theorem""; ""1.13.3 Exponential branching clock""; ""1.14 Branching diffusion""; ""1.14.1 When the branching rate is bounded from above""; ""1.14.2 The branching Markov property""; ""1.14.3 Requiring only that λc <�""; ""1.14.4 The branching Markov property; general case""; ""1.14.5 Further properties""
- 1.14.6 Local extinction1.14.7 Four useful results on branching diffusions
- 1.14.8 Some more classes of elliptic operators/branching diffusions
- 1.14.9 Ergodicity
- 1.15 Super-Brownian motion and superdiffusions
- 1.15.1 Superprocess via its Laplace functional
- 1.15.2 The particle picture for the superprocess
- 1.15.3 Super-Brownian motion
- 1.15.4 More general branching
- 1.15.5 Local and global behavior
- 1.15.6 Space-time H-transform; weighted superprocess
- 1.16 Exercises
- 1.17 Notes
- ""2. The Spine Construction and the SLLN for branching diffusions""""2.1 Setting""; ""2.2 Local extinction versus local exponential growth""; ""2.3 Some motivation""; ""2.4 The â€?spineâ€?""; ""2.4.1 The spine change of measure""; ""2.4.2 The â€?spine decompositionâ€? of the martingale WÏ?""; ""2.5 The Strong law""; ""2.5.1 The Lp-convergence of the martingale""; ""2.5.2 Proof of Theorem 2.2 along lattice times""; ""2.5.3 Replacing lattice times with continuous time""; ""2.5.4 Proof of the Weak Law (Theorem 2.3)""; ""2.6 Exercises""; ""2.7 Notes""; ""3. Examples of The Strong Law""