Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak convergence of the function-indexed integrated periodogram for
  infinite variance processes   In this paper, we study the weak convergence of the integrated periodogram
indexed by classes of functions for linear processes with symmetric
$\alpha$-stable innovations. Under suitable summability conditions on the
series of the Fourier coefficients of the index functions, we show that the
weak limits constitute $\alpha$-stable processes which have representations as
infinite Fourier series with i.i.d. $\alpha$-stable coefficients. The cases
$\alpha\in(0,1)$ and $\alpha\in[1,2)$ are dealt with by rather different
methods and under different assumptions on the classes of functions. For
example, in contrast to the case $\alpha\in(0,1)$, entropy conditions are
needed for $\alpha\in[1,2)$ to ensure the tightness of the sequence of
integrated periodograms indexed by functions. The results of this paper are of
additional interest since they provide limit results for infinite mean random
quadratic forms with particular Toeplitz coefficient matrices.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph