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Quantum open systems are described in the Markovian limit by master equationsin Lindblad form. I argue that common ``quantum trajectory'' techniquescorresponding to continuous measurement schemes, which solve the masterequation by unraveling its evolution into stochastic trajectories in Hilbertspace, correspond closely to particular sets of decoherent (or consistent)histories. This is illustrated by a simple model of photon counting. Anequivalence is shown for these models between standard quantum jumps and theorthogonal jumps of Di\'osi, which have already been shown to correspond todecoherent histories. This correspondence is compared to simple treatments oftrajectories based on repeated or continuous measurements.Comment: 31 pages RevTeX 3.1 + 2 figures (postscript). Extensive revisions,  with new material. Submitted to Phys. Rev.

Continuous measurements, quantum trajectories, and decoherent histories