Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Karhunen-Lo\`eve expansion for a generalization of Wiener bridge   We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t -
g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a
standard Wiener process and $g:[0,1]\to R$ is a twice continuously
differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This
process is an important limit process in the theory of goodness-of-fit tests.
We formulate two special cases with the function
$g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$,
respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from
$0$ to $0$.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph