  The behavior of the most probable values of the order parameter $x$ and the
amplitude $\phi$ of conjugate force fluctuations is studied for a stochastic
system with a colored multiplicative noise with absorbing states. The phase
diagrams introduced as dependencies the noise self-correlation time vs
temperature and noise growth velocity are defined. It is shown that phase
half-plane $(x,\phi)$ can be split into isolated domains of large,
intermediate, and small values of $x$. System behavior in these domains is
studied by the probability represented as path integral. In the region $x\ll
1$, the trajectories converge to the point $x = \phi = 0$ for $0 < a < 1/2$ and
to $x = 0$, $\phi\to\infty$ for $1/2 < a \le 1$. In the former case, the
probability of realization of trajectories is finite, while in the latter case
it is vanishingly small, and an absorbing state can be formed.
