  The paper investigates data-driven output-feedback predictive control of
linear systems subject to stochastic disturbances. The scheme relies on the
recursive solution of a suitable data-driven reformulation of a stochastic
Optimal Control Problem (OCP), which allows for forward prediction and
optimization of statistical distributions of inputs and outputs. Our approach
avoids the use of parametric system models. Instead it is based on previously
recorded data using a recently proposed stochastic variant of Willems'
fundamental lemma. The stochastic variant of the lemma is applicable to a large
class of linear dynamics subject to stochastic disturbances of Gaussian and
non-Gaussian nature. To ensure recursive feasibility, the initial condition of
the OCP -- which consists of information about past inputs and outputs -- is
considered as an extra decision variable of the OCP. We provide sufficient
conditions for recursive feasibility and closed-loop practical stability of the
proposed scheme as well as performance bounds. Finally, a numerical example
illustrates the efficacy and closed-loop properties of the proposed scheme.
