High-performance real-time applications, expected to be of importance in the upcoming 5G era, such as virtual and augmented reality or tele-presence, have stringent requirements on throughput and per-packet in-order delivery delay. Use of multipath transport is gaining momentum for supporting these applications. However, building an efficient, low latency multipath transfer mechanism remains highly challenging. The primary reason for this is that the delivery delay along each path is typically uncertain and time-varying. When the transmitter ignores the stochastic nature of the path delays, then packets sent along different paths frequently arrive out of order and need to be buffered at the receiver to allow in-order delivery to the application. In this paper, we propose Stochastic Earliest Delivery Path First (S-EDPF), a generalization of EDPF which takes into account uncertainty and time-variation in path delays yet has low-complexity suited to practical implementation. Moreover, we integrate a novel low-delay Forward Error Correction (FEC) scheme into S-EDPF in a principled manner by deriving the optimal schedule for coded packets across multiple paths. Finally, we demonstrate, both analytically and empirically, that S-EDPF is effective at mitigating the delay impact of reordering and loss in multipath transport protocols, offering substantial performance gains over the state of the art.