  Finite $N$-unit Langevin models with additive and multiplicative noises have
been studied with the use of the augmented moment method (AMM) previously
proposed by the author [H. Hasegawa, Phys. Rev E {\bf 67}, 041903 (2003)].
Original $N$-dimensional stochastic equations are transformed to the
three-dimensional deterministic equations for means and fluctuations of local
and global variables. Calculated results of our AMM are in good agreement with
those of direct simulations (DS). We have shown that although the effective
strength of the additive noise of the $N$-unit system is scaled as
$\beta(N)=\beta(1)/\sqrt{N}$, it is not the case for multiplicative noise
[$\alpha(N) \neq \alpha(1)/\sqrt{N}$], where $\alpha(N)$ and $\beta(N)$ denote
the strength of multiplicative and additive noises, respectively, for the
size-$N$ system. It has been pointed out that the naive assumption of
$\alpha(N) = \alpha(1)/\sqrt{N}$ leads to result which violates the
central-limit theorem and which does not agree with those of DS and AMM.
