Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An It\^o's type formula for the fractional Brownian motion in Brownian
  time   Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in
(0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional
Brownian motion in Brownian motion time (of index $H$), recently studied in
\cite{13}, is by definition the process $Z=X\circ Y$. It is a continuous,
non-Gaussian process with stationary increments, which is selfsimilar of index
$H/2$. The main result of the present paper is an It\^{o}'s type formula for
$f(Z_t)$, when $f:\R\to\R$ is smooth and $H\in [1/6,1)$. When $H>1/6$, the
change-of-variable formula we obtain is similar to that of the classical
calculus. In the critical case $H=1/6$, our change-of-variable formula is in
law and involves the third derivative of $f$ as well as an extra Brownian
motion independent of the pair $(X,Y)$. We also discuss briefly the case
$H<1/6$.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat