Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The compact support property for measure-valued diffusions   The purpose of this article is to give a rather thorough understanding of the
compact support property for measure-valued diffusion processes corresponding
to semi-linear equations of the form \[& u_t=Lu+\beta u-\alpha u^p \text{in}
R^d\times (0,\infty), p\in(1,2]; &u(x,0)=f(x) \text{in} R^d; &u(x,t)\ge0
\text{in} R^d\times[0,\infty). \] In particular, we shall investigate how the
interplay between the underlying motion (the diffusion process corresponding to
$L$) and the branching affects the compact support property. In \cite{EP99},
the compact support property was shown to be equivalent to a certain analytic
criterion concerning uniqueness of the Cauchy problem for the semilinear
parabolic equation related to the measured valued diffusion. In a subsequent
paper \cite{EP03}, this analytic property was investigated purely from the
point of view of partial differential equations. Some of the results obtained
in this latter paper yield interesting results concerning the compact support
property. In this paper, the results from \cite{EP03} that are relevant to the
compact support property are presented, sometimes with extensions. These
results are interwoven with new results and some informal heuristics. Taken
together, they yield a fairly comprehensive picture of the compact support
property. \it Inter alia\rm, we show that the concept of a measure-valued
diffusion \it hitting\rm a point can be investigated via the compact support
property, and suggest an alternate proof of a result concerning the hitting of
points by super-Brownian motion.

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The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int