1,011 research outputs found
A superprocess involving both branching and coalescing
We consider a superprocess with coalescing Brownian spatial motion. We first
prove a dual relationship between two systems of coalescing Brownian motions.
In consequence we can express the Laplace functionals for the superprocess in
terms of coalescing Brownian motions, which allows us to obtain some explicit
results. We also point out several connections between such a superprocess and
the Arratia flow. A more general model is discussed at the end of this paper.Comment: 25 page
Stepping-stone model with circular Brownian migration
In this paper we consider a stepping-stone model on a circle with circular
Brownian migration. We first point out a connection between Arratia flow and
the marginal distribution of this model. We then give a new representation for
the stepping-stone model using Arratia flow and circular coalescing Brownian
motion. Such a representation enables us to carry out some explicit
computation. In particular, we find the Laplace transform for the time when
there is only a single type left across the circle.Comment: 12 page
The compact support property for the -Fleming-Viot process with underlying Brownian motion
Using the lookdown construction of Donnelly and Kurtz we prove that, at any
fixed positive time, the -Fleming-Viot process with underlying
Brownian motion has a compact support provided that the corresponding
-coalescent comes down from infinity not too slowly. We also find both
upper bound and lower bound on the Hausdorff dimension for the support.Comment: 21 page
Balls-in-boxes duality for coalescing random walks and coalescing Brownian motions
We present a duality relation between two systems of coalescing random walks
and an analogous duality relation between two systems of coalescing Brownian
motions. Our results extends previous work in the literature and we apply it to
the study of a system of coalescing Brownian motions with Poisson immigration.Comment: 13 page
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