  This paper studies Langevin equation with random damping due to
multiplicative noise and its solution. Two types of multiplicative noise,
namely the dichotomous noise and fractional Gaussian noise are considered.
Their solutions are obtained explicitly, with the expressions of the mean and
covariance determined explicitly. Properties of the mean and covariance of the
Ornstein-Uhlenbeck process with random damping, in particular the asymptotic
behavior, are studied. The effect of the multiplicative noise on the stability
property of the resulting processes is investigated.
