  The author studied the growth of the amplitude in a Mathieu-like equation
with multiplicative white noise. The approximate value of the exponent at the
extremum on parametric resonance regions was obtained theoretically by
introducing the width of time interval, and the exponents were calculated
numerically by solving the stochastic differential equations by a symplectic
numerical method. The Mathieu-like equation contains a parameter $\alpha$ that
is determined by the intensity of noise and the strength of the coupling
between the variable and the noise. The value of $\alpha$ was restricted not to
be negative without loss of generality. It was shown that the exponent
decreases with $\alpha$, reaches a minimum and increases after that. It was
also found that the exponent as a function of $\alpha$ has only one minimum at
$\alpha \neq 0$ on parametric resonance regions of $\alpha = 0$. This minimum
value is obtained theoretically and numerically. The existence of the minimum
at $\alpha \neq 0$ indicates the suppression of the growth by multiplicative
white noise.
