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Bücher Englische Bücher Spatial Branching Processes, Random Snakes and Partial Differential Equations
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Spatial Branching Processes, Random Snakes and Partial Differential Equations
Jean-Francois Le Gall (Taschenbuch, Englisch)
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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. 53,49 €
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Technische Daten
Erscheinungsdatum
01.07.1999
Sprache
Englisch
EAN
9783764361266, 9783764361266
Herausgeber
Springer Basel
Serien- oder Bandtitel
Lectures in Mathematics. ETH Zürich
Sonderedition
Nein
Autor
Jean-Francois Le Gall
Seitenanzahl
163
Auflage
1
Einbandart
Taschenbuch
Schlagwörter
PDE, Probability theory, Stochastics, classification, mechanics, partial differential equation
Thema-Inhalt
PBW - Angewandte Mathematik
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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