Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On properties of a class of strong limits for supercritical
  superprocesses   Suppose that $X=\{X_t, t\ge 0; \mathbb{P}_{\mu}\}$ is a supercritical
superprocess in a locally compact separable metric space $E$. Let $\phi_0$ be a
positive
  eigenfunction corresponding to the first eigenvalue $\lambda_0$ of the
generator of the mean semigroup of $X$. Then
$M_t:=e^{-\lambda_0t}\langle\phi_0, X_t\rangle$ is a positive martingale. Let
$M_\infty$ be the limit of $M_t$. It is known that $M_\infty$ is non-degenerate
iff the $L\log L$ condition is satisfied. When the $L\log L$ condition may not
be satisfied, we recently proved in (arXiv:1708.04422) that there exist a
non-negative function $\gamma_t$ on $[0, \infty)$ and a non-degenerate random
variable $W$ such that for any finite nonzero Borel measure $\mu$ on $E$, $$
\lim_{t\to\infty}\gamma_t\langle \phi_0,X_t\rangle
=W,\qquad\mbox{a.s.-}\mathbb{P}_{\mu}. $$ In this paper, we mainly investigate
properties of $W$. We prove that $W$ has strictly positive density on
$(0,\infty)$. We also investigate the small value probability and tail
probability problems of $W$.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org