  We investigate the effects of white noise on parametric resonance in $\lambda
\phi^{4}$ theory. The potential $V(\phi)$ in this study is ${1/2} m^{2}
\phi^{2} + {1/3} g \phi^{3} + {1/4} \lambda \phi^{4}$. An Mathieu-like equation
is derived and the derived equation is applied to a partially thermalized
system. The magnitudes of the amplifications are extracted by solving the
equations numerically for various values of parameters. It is found that the
amplification is suppressed by white noise in almost all the cases. However, in
some $g=0$ cases, the amplification with white noise is slightly stronger than
that without white noise. In the $g=0$ cases, the fields are always amplified.
The amplification is maximal at $k_{m} \neq 0$ in some $g=0$ cases. Contrarily,
in the $g = {3 \sqrt{2 \lambda} m}/{2}$ cases, the fields for some finite modes
are suppressed and the amplification is maximal at $k_{m} \sim 0$ when the
amplification occurs. It is possible to distinguish by these differences
whether the system is on the $g=0$ state or not.
