Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional limit theorem for the self-intersection local time of the
  fractional Brownian motion   Let $\{B_{t}\}_{t\geq0}$ be a $d$-dimensional fractional Brownian motion with
Hurst parameter $0<H<1$, where $d\geq2$. Consider the approximation of the
self-intersection local time of $B$, defined as \begin{align*}
I_{T}^{\varepsilon}
  &=\int_{0}^{T}\int_{0}^{t}p_{\varepsilon}(B_{t}-B_{s})dsdt, \end{align*}
where $p_\varepsilon(x)$ is the heat kernel. We prove that the process
$\{I_{T}^{\varepsilon}-\mathbb{E}\left[I_{T}^{\varepsilon}\right]\}_{T\geq0}$,
rescaled by a suitable normalization, converges in law to a constant multiple
of a standard Brownian motion for $\frac{3}{2d}<H\leq\frac{3}{4}$ and to a
multiple of a sum of independent Hermite processes for $\frac{3}{4}<H<1$, in
the space $C[0,\infty)$, endowed with the topology of uniform convergence on
compacts.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin