  We show that the effect of a Gaussian Bosonic environment linearly coupled to
a quantum system can be simulated by a stochastic Lindblad master equation
characterized by a set of ancillary Bosonic modes initially at zero temperature
and classical stochastic fields. We test the method for Ohmic environments with
exponential and polynomial cut-offs against, respectively, the Hierarchical
Equations of Motion and the deterministic pseudomode model with respect to
which the number of ancillary quantum degrees of freedom is reduced. For a
subset of rational spectral densities, all parameters are explicitly specified
without the need of any fitting procedure, thereby simplifying the modeling
strategy. Interestingly, the classical fields in this decomposition must
sometimes be imaginary-valued, which can have counter-intuitive effects on the
system properties which we demonstrate by showing that they can decrease the
entropy of the system, in contrast to real-valued fields.
