Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the inverse problem of fractional Brownian motion and the inverse of
  infinite Toeplitz matrices   The inverse problem of fractional Brownian motion and other Gaussian
processes with stationary increments involves inverting an infinite hermitian
positively definite Toeplitz matrix (a matrix that has equal elements along its
diagonals). The problem of inverting Toeplitz matrices is interesting on its
own and has various applications in physics, signal processing, statistics,
etc. A large body of literature has emerged to study this question since the
seminal work of Szeg\"o on Toeplitz forms in 1920's. In this paper we obtain,
for the first time, an explicit general formula for the inverse of infinite
hermitian positive definite Toeplitz matrices. Our formula is explicitly given
in terms of the Szeg\"o function associated to the spectral density of the
matrix. These results are applied to the fractional Brownian motion and to
$m$-diagonal Toeplitz matrices and we provide explicit examples.

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The categories of this paper are: comp-gas
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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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: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph