Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General solution of the Poisson equation for Quasi-Birth-and-Death
  processes   We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where
$P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with
infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm
u$ is the unknown. Our main result is to provide the general solution of this
equation. To this purpose we use the block tridiagonal and block Toeplitz
structure of the matrix $P$ to obtain a set of matrix difference equations,
which are solved by constructing suitable resolvent triples.

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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org