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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 (Yt, t ≥ 0). More precisely: Eω0(〈h,Yt〉) = 〈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 Yt increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of ‘boundary condition’, namely an equivalence relation on the set of infinite paths of
the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree of a
branching process. What is the...
In this paper, we indicate how integer-valued autoregressive time
series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching
processes with immigration. This allows the derivation of a simple criteria for the
existence of a stationary distribution of the time series, thus proving and extending
some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour
[11]. One can then transfer results on estimation in subcritical multitype branching
processes to stationary...
A branching random motion on a line, with abrupt changes of direction,
is studied. The branching mechanism, being independent
of random motion, and intensities of reverses are defined by a particle's
current direction. A solution of a certain hyperbolic system of coupled
non-linear equations (Kolmogorov type backward equation) has
a so-called McKean representation via such processes.
Commonly this system possesses travelling-wave solutions.
The convergence of solutions with Heaviside terminal...
We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description of the...
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