Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse source problems for the stochastic wave equations: far-field
  patterns   This paper addresses the direct and inverse source problems for the
stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in
a unified framework. The driven source is assumed to be a centered generalized
microlocally isotropic Gaussian random field, whose covariance and relation
operators are classical pseudo-differential operators. Given the random source,
the direct problems are shown to be well-posed in the sense of distributions
and the regularity of the solutions are given. For the inverse problems, we
demonstrate by ergodicity that the principal symbols of the covariance and
relation operators can be uniquely determined by a single realization of the
far-field pattern averaged over the frequency band with probability one.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th