  We have discussed the dynamics of Langevin model subjected to colored noise,
by using the functional-integral method (FIM) combined with equations of motion
for mean and variance of the state variable. Two sets of colored noise have
been investigated: (a) one additive and one multiplicative colored noise, and
(b) one additive and two multiplicative colored noise. The case (b) is examined
with the relevance to a recent controversy on the stationary subthreshold
voltage distribution of an integrate-and-fire model including stochastic
excitatory and inhibitory synapses and a noisy input. We have studied the
stationary probability distribution and dynamical responses to time-dependent
(pulse and sinusoidal) inputs of the linear Langevin model. Model calculations
have shown that results of the FIM are in good agreement with those of direct
simulations (DSs). A comparison is made among various approximate analytic
solutions such as the universal colored noise approximation (UCNA). It has been
pointed out that dynamical responses to pulse and sinusoidal inputs calculated
by the UCNA are rather different from those of DS and the FIM, although they
yield the same stationary distribution.
