This study addresses a stochastic model predictive tracking problem for linear parameter-varying (LPV) systems described by affine parameter-dependent state-space representations and additive stochastic uncertainties. The reference trajectory is considered as a piecewise constant signal and assumed to be known at all time instants. To obtain prediction equations, the scheduling signal is usually assumed to be constant or its variation is assumed to belong to a convex set. In this study, the underlying scheduling signal is given a stochastic description during the prediction horizon, which aims to overcome the shortcomings of the two former characterisations, namely restrictiveness and conservativeness. Hence, the overall LPV system dynamics consists of additive and multiplicative noise terms up to second order. Due to the presence of stochastic disturbances, probabilistic state constraints are considered. Since the disturbances make the computation of prediction dynamics difficult, augmented state prediction dynamics are considered, by which, feasibility of probabilistic constraints and closed-loop stability are addressed. The overall approach is illustrated using a tank system model.