Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rate for a class of supercritical superprocesses   Suppose $X=\{X_t, t\ge 0\}$ is a supercritical superprocess. Let $\phi$ be
the non-negative eigenfunction of the mean semigroup of $X$ corresponding to
the principal eigenvalue $\lambda>0$. Then $M_t(\phi)=e^{-\lambda
t}\langle\phi, X_t\rangle, t\geq 0,$ is a non-negative martingale with almost
sure limit $M_\infty(\phi)$. In this paper we study the rate at which
$M_t(\phi)-M_\infty(\phi)$ converges to $0$ as $t\to \infty$ when the process
may not have finite variance. Under some conditions on the mean semigroup, we
provide sufficient and necessary conditions for the rate in the almost sure
sense. Some results on the convergence rate in $L^p$ with $p\in(1, 2)$ are also
obtained.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph