Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random-field Solutions to Linear Hyperbolic Stochastic Partial
  Differential Equations with Variable Coefficients   In this article we show the existence of a random-field solution to linear
stochastic partial differential equations whose partial differential operator
is hyperbolic and has variable coefficients that may depend on the temporal and
spatial argument. The main tools for this, pseudo-differential and Fourier
integral operators, come from microlocal analysis. The equations that we treat
are second-order and higher-order strictly hyperbolic, and second-order weakly
hyperbolic with uniformly bounded coefficients in space. For the latter one we
show that a stronger assumption on the correlation measure of the random noise
might be needed. Moreover, we show that the well-known case of the stochastic
wave equation can be embedded into the theory presented in this article.

11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg