Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lecture Notes on Stationary Gamma Processes   For each $\lambda>0$ and every square-integrable infinitely-divisible (ID)
distribution there exists at least one stationary stochastic process $t\mapsto
X_t$ with the specified distribution for $X_1$ and with first-order
autoregressive (AR(1)) structure in the sense that the autocorrelation of $X_s$
and $X_t$ is $\exp(-\lambda|s-t|)$ for all indices $s,t$. For the special case
of the standard Normal distribution, the process $X_t$ is unique -- namely, the
first-order autoregressive Ornstein-Uhlenbeck velocity process. The process
$X_t$ is also uniquely determined if $X_1$ is accorded the unit rate Poisson
distribution.
  For the Gamma distribution, however, $X_t$ is \emph{not} determined uniquely.
In these lecture notes we describe six distinct processes with the same
univariate marginal distributions and AR(1) autocorrelation function. We
explore a few of their properties and describe methods of simulating their
sample paths.

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The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat