Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak convergence rates for spatial spectral Galerkin approximations of
  semilinear stochastic wave equations with multiplicative noise   Stochastic wave equations appear in several models for evolutionary processes
subject to random forces, such as the motion of a strand of DNA in a liquid or
heat flow around a ring. Semilinear stochastic wave equations can typically not
be solved explicitly, but the literature contains a number of results which
show that numerical approximation processes converge with suitable rates of
convergence to solutions of such equations. In the case of approximation
results for strong convergence rates, semilinear stochastic wave equations with
both additive or multiplicative noise have been considered in the literature.
In contrast, the existing approximation results for weak convergence rates
assume that the diffusion coefficient of the considered semilinear stochastic
wave equation is constant, that is, it is assumed that the considered wave
equation is driven by additive noise, and no approximation results for
multiplicative noise are known. The purpose of this work is to close this gap
and to establish sharp weak convergence rates for semilinear stochastic wave
equations with multiplicative noise. In particular, our weak convergence result
establishes as a special case essentially sharp weak convergence rates for the
hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov
equation, the H\"older-inequality for Schatten norms, and the mild It\^o
formula.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an