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Erschienen in:
1999 | OriginalPaper | Buchkapitel
Exit Measures and the Nonlinear Dirichlet Problem
verfasst von : Jean-François Le Gall
Erschienen in: Spatial Branching Processes, Random Snakes and Partial Differential Equations
Verlag: Birkhäuser Basel
Enthalten in: Professional Book Archive
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In this chapter we use the Brownian snake approach of the previous chapter to construct the exit measure of quadratic superprocesses. In the special case where the spatial motion is Brownian motion in ℝd, the exit measure yields a probabilistic solution of the Dirichlet problem associated with the equation Δu = u2 in a regular domain. This probabilistic solution plays a major role in further developments that will be presented in the following chapters.