  We present a formalism for calculating the non-symmetrized quantum current
noise within the Born-Markov approximation for the master equation. The
formalism is particularly well suited to obtaining the current noise for
quantum transport in mesoscopic devices such as a superconducting single
electron transistor (SSET). As an example of the method, we obtain explicit
results for the double Josephson-quasiparticle (DJQP) resonance in a SSET. Our
calculations reveal the asymmetries that develop in the current noise as well
as clarifying the behavior at high frequencies. Our findings are consistent
with recent measurements of the asymmetry in the current noise spectrum.
