Spatial Branching Processes, Random Snakes and Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1999
|
| Schriftenreihe: | Lectures in Mathematics ETH Zürich
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In these lectures, we give an account of certain recent developments of the theory of spatial branching processes. These developments lead to several fas cinating probabilistic objects, which combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial dif ferential equations. Our first objective is to give a short self-contained presentation of the measure valued branching processes called superprocesses, which have been studied extensively in the last twelve years. We then want to specialize to the important class of superprocesses with quadratic branching mechanism and to explain how a concrete and powerful representation of these processes can be given in terms of the path-valued process called the Brownian snake. To understand this representation as well as to apply it, one needs to derive some remarkable properties of branching trees embedded in linear Brownian motion, which are of independent interest. A nice application of these developments is a simple construction of the random measure called ISE, which was proposed by Aldous as a tree-based model for random distribution of mass and seems to play an important role in asymptotics of certain models of statistical mechanics. We use the Brownian snake approach to investigate connections between super processes and partial differential equations. These connections are remarkable in the sense that almost every important probabilistic question corresponds to a significant analytic problem |
| Beschreibung: | 1 Online-Ressource (163p) |
| ISBN: | 9783034886833 9783764361266 |
| DOI: | 10.1007/978-3-0348-8683-3 |
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| discipline | Mathematik |
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| isbn | 9783034886833 9783764361266 |
| language | English |
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| spelling | Gall, Jean-François Verfasser aut Spatial Branching Processes, Random Snakes and Partial Differential Equations by Jean-François Gall Basel Birkhäuser Basel 1999 1 Online-Ressource (163p) txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics ETH Zürich In these lectures, we give an account of certain recent developments of the theory of spatial branching processes. These developments lead to several fas cinating probabilistic objects, which combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial dif ferential equations. Our first objective is to give a short self-contained presentation of the measure valued branching processes called superprocesses, which have been studied extensively in the last twelve years. We then want to specialize to the important class of superprocesses with quadratic branching mechanism and to explain how a concrete and powerful representation of these processes can be given in terms of the path-valued process called the Brownian snake. To understand this representation as well as to apply it, one needs to derive some remarkable properties of branching trees embedded in linear Brownian motion, which are of independent interest. A nice application of these developments is a simple construction of the random measure called ISE, which was proposed by Aldous as a tree-based model for random distribution of mass and seems to play an important role in asymptotics of certain models of statistical mechanics. We use the Brownian snake approach to investigate connections between super processes and partial differential equations. These connections are remarkable in the sense that almost every important probabilistic question corresponds to a significant analytic problem Mathematics Mathematics, general Mathematik Verzweigungsprozess (DE-588)4188184-9 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Verzweigungsprozess (DE-588)4188184-9 s Stochastische partielle Differentialgleichung (DE-588)4135969-0 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8683-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gall, Jean-François Spatial Branching Processes, Random Snakes and Partial Differential Equations Mathematics Mathematics, general Mathematik Verzweigungsprozess (DE-588)4188184-9 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4188184-9 (DE-588)4135969-0 |
| title | Spatial Branching Processes, Random Snakes and Partial Differential Equations |
| title_auth | Spatial Branching Processes, Random Snakes and Partial Differential Equations |
| title_exact_search | Spatial Branching Processes, Random Snakes and Partial Differential Equations |
| title_full | Spatial Branching Processes, Random Snakes and Partial Differential Equations by Jean-François Gall |
| title_fullStr | Spatial Branching Processes, Random Snakes and Partial Differential Equations by Jean-François Gall |
| title_full_unstemmed | Spatial Branching Processes, Random Snakes and Partial Differential Equations by Jean-François Gall |
| title_short | Spatial Branching Processes, Random Snakes and Partial Differential Equations |
| title_sort | spatial branching processes random snakes and partial differential equations |
| topic | Mathematics Mathematics, general Mathematik Verzweigungsprozess (DE-588)4188184-9 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Verzweigungsprozess Stochastische partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-3-0348-8683-3 |
| work_keys_str_mv | AT galljeanfrancois spatialbranchingprocessesrandomsnakesandpartialdifferentialequations |