  A systematic procedure for deriving the master equation of a dissipative
system is reported in the framework of stochastic description. For the
Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and
elementary derivation of the bath-induced stochastic field is presented. The
dynamics of the system is thereby fully described by a stochastic differential
equation and the desired master equation would be acquired with statistical
averaging. It is shown that the existence of a closed-form master equation
depends on the specificity of the system as well as the feature of the
dissipation characterized by the spectral density function. For a dissipative
harmonic oscillator it is observed that the correlation between the stochastic
field due to the bath and the system can be decoupled and the master equation
naturally comes out. Such an equation possesses the Lindblad form in which time
dependent coefficients are determined by a set of integral equations. It is
proved that the obtained master equation is equivalent to the well-known
Hu-Paz-Zhang equation based on the path integral technique. The procedure is
also used to obtain the master equation of a dissipative harmonic oscillator in
time-dependent fields.
