Displaying similar documents to “A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees”

Branching process associated with 2d-Navier Stokes equation.

Saïd Benachour, Bernard Roynette, Pierre Vallois (2001)

Revista Matemática Iberoamericana

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Ω being a bounded open set in R, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Y, t ≥ 0). More precisely: E(〈h,Y〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Y increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation...

A lattice gas model for the incompressible Navier–Stokes equation

J. Beltrán, C. Landim (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.

Invariance principles for spatial multitype Galton–Watson trees

Grégory Miermont (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that critical multitype Galton–Watson trees converge after rescaling to the brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show...