  The quantum analog of the joint probability distributions describing a
classical stochastic process is introduced. A prescription is given for
constructing the quantum distribution associated with a sequence of
measurements. For the case of quantum Brownian motion this prescription is
illustrated with a number of explicit examples. In particular it is shown how
the prescription can be extended in the form of a general formula for the
Wigner function of a Brownian particle entangled with a heat bath.
