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Stochastic Schr{\"o}dinger equations for quantum trajectories offer analternative and sometimes superior approach to the study of open quantum systemdynamics. Here we show that recently established convolutionless non-Markovianstochastic Schr{\"o}dinger equations may serve as a powerful tool for thederivation of convolutionless master equations for non-Markovian open quantumsystems. The most interesting example is quantum Brownian motion (QBM) of aharmonic oscillator coupled to a heat bath of oscillators, one of themost-employed exactly soluble models of open system dynamics. We showexplicitly how to establish the direct connection between the exactconvolutionless master equation of QBM and the corresponding convolutionlessexact stochastic Schr\"odinger equation.Comment: 18 pages, RevTe

Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion