  Systems described by equations involving both multiplicative and additive
noise are common in nature. Examples include convection of a passive scalar
field, polymersin turbulent flow, and noise in dye lasers. In this paper the
one component version of this problem is studied. The steady state probability
distribution is classified into two different types of behavior. One class has
power law tails and the other is of the form of an exponential to a power law.
The value of the power law exponent is determined analytically for models
having colored gaussian noise. It is found to only depend on the power spectrum
of the noise at zero frequency. When non-gaussian noise is considered it is
shown that stretched exponential tails are possible. An intuitive understanding
of the results is found and makes use of the Lyapunov exponents for these
systems.
