In classical stochastic analysis the stochastic derivative
of a polynomial function $f$ of integrator process ${\bf
\Lambda}=(\Lambda_1,\cdots ,\Lambda_N)$ whose differentials
satisfy a closed Ito multiplication table can be expressed
as $$ df({\bf \Lambda})=f({\bf \Lambda}+d{\bf
\Lambda})-f({\bf \Lambda}), $$ and leads to a chaotic
decomposition of $f({\bf \Lambda})$. In quantum theories the
Ito table becomes noncommutative but the same formula and
the corresponding chaotic decomposition hold formally for
elements of the universal enveloping algebra ${\cal U}$ of
the Lie algebra formed by the Ito differentials, and acquire
rigorous meaning in terms of the coproduct structure of
${\cal U}$.