The Wiener process (say, on $\mathbb{R}$) can be thought of as a scaling limit of a classical, discrete random walk. On the other hand, one can define and study *quantum random walks*, when the underlying stochastic process is governed by a unitary transform + measurement (for an excellent introduction, see http://arxiv.org/abs/quant-ph/0303081).

My question is - do quantum random walks have a reasonable continuous limit, something which would give a quantum analogue of the Wiener process?