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" Spatial branching processes, random snakes, and partial differential equations "
Jean-François Le Gall.
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BL
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721913
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b541621
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| Main Entry
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Jean-François Le Gall.
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| Title & Author
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Spatial branching processes, random snakes, and partial differential equations\ Jean-François Le Gall.
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| Publication Statement
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Basel ; Boston: Birkhäuser, ©1999.
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| Series Statement
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Lectures in mathematics ETH Zürich.
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viii, 162 Seiten : Diagramme ; 24 cm.
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| ISBN
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0817661263
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: 3764361263
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: 9780817661267
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: 9783764361266
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| Contents
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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 Ito 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 representation theorem.- VII.4 Further developments.- VIII Levy Processes and the Genealogy of General Continuous-state Branching Processes.- VIII.1 The discrete setting.- VIII.2 Levy processes.- VIII.3 The height process.- VIII.4 The exploration process.- VIII.5 Proof of Theorem 2.- Bibliographical Notes.
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| Subject
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Stochastische partielle Differentialgleichung.
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Verzweigungsprozess -- Stochastischer Prozess.
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Verzweigungsprozess.
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| LC Classification
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QA274.76J436 1999
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| Added Entry
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Jean-François Le Gall
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