Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact moduli of continuity for general chi--square processes and for
  permanental processes related to the Ornstein--Uhlenbeck process   Let $ \overline B=\{ \overline B_{t},t\in R^{1} \}$ be Brownian motion killed
after an independent exponential time with mean $2/\lambda^{2}$. The process
$\overline B$ has potential densities, \[
  u(x,y) ={e^{-\lambda |y-x|}\over \lambda},\qquad x,y\in R^{ 1}, \] which is
also the covariance of an Ornstein--Uhlenbeck process. Let $f$ be an excessive
function for $\overline B$. Then,
  \[
  {e^{-\lambda |y-x|}\over \lambda}+f(y),\qquad x,y\in R^{ 1}, \]
  is the kernel of an $\alpha$-permanental process $ X_{\alpha}=\{
X_{\alpha}(t), t\in R^{ 1}\}$ for all $\alpha>0$. It is shown that for all
$k\ge 1$ and intervals $\Delta \subseteq [0,1] $, \[
  \limsup_{h\to 0}\sup_{\stackrel{|u-v|\le h }{ u,v\in\Delta}} \frac{|X_{k/2}
(u)-X_{k/2} (v)|}{ 2 ( |u-v| \log 1/|u-v|)^{1/2}}= \sqrt 2
\sup_{t\in\Delta}X_{k/2}^{1/2}(t)\qquad a.s.\] The local modulus of continuity
of $X_{k/2}$ for all $k\ge 1$ is also obtained.
  Local and uniform moduli of continuity are also obtained for chi--square
processes which are defined by,
  \[
  Y_{k/2}(t)=\sum_{i=1}^{k}\frac{\eta^2_{i}(t)}{2},\qquad t\in [0,1],
  \]
  where $\eta=\{\eta(t);t\in [0,1]\}$ is a mean zero Gaussian process and
$\{\eta_{i};i=1,\ldots, k\}$ are independent copies of $\eta.$

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The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys