  We investigate the amplification of the field induced by white noise. In the
present study, we study a stochastic equation which has two parameters, the
energy $\omega(\vec{k})$ of a free particle and the coupling strength $D$
between the field and white noise, where the quantity $\vec{k}$ represents the
momentum of a free particle. This equation is reduced to the equation with one
parameter $\alpha(\vec{k})$ which is defined as $\alpha(\vec{k}) = D
(\omega(\vec{k}))^{-3/2}$. We obtain the expression of the exponent
statistically averaged over the unit time and derive an approximate expression
of it. In addition, the exponent is obtained numerically by solving the
stochastic equation. We find that the amplification increases with
$\alpha(\vec{k})$. This indicates that white noise can amplify the fields for
soft modes if the mass $m$ of the field is sufficiently light and if the
strength of the coupling between the field and white noise is sufficiently
strong, when the energy $\omega(\vec{k})$ is equal to $\sqrt{m^{2} +
\vec{k}^{2}}$. We show that the $\alpha(\vec{k})$ dependence of the exponent
statistically averaged is qualitatively similar to that of the exponent
obtained by solving the stochastic equation numerically, and that these two
exponents for the small value of $\alpha(\vec{k})$ are quantitatively similar.
