  We derive and solve analytically the non-Markovian master equation for
harmonic quantum Brownian motion proving that, for weak system-reservoir
couplings and high temperatures, it can be recast in the form of the master
equation for a harmonic oscillator interacting with a squeezed thermal bath.
This equivalence guarantees preservation of positivity of the density operator
during the time evolution and allows one to establish a connection between the
dynamics of Schr\"odinger cat states in squeezed environments and
environment-induced decoherence in quantum Brownian motion.
