  An extension of the Born rule, the {\it quantum typicality rule}, has
recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly
speaking, this rule states that if the wave function of a particle is split
into non-overlapping wave packets, the particle stays approximately inside the
support of one of the wave packets, without jumping to the others.
  In this paper a formal definition of this rule is given in terms of {\it
imprecise probability}. An imprecise probability space is a measurable space
$(\Omega, {\cal A})$ endowed with a {\it set} of probability measures $\cal P$.
The quantum formalism and the quantum typicality rule allow us to define a set
of probabilities ${\cal P}_\Psi$ on $(X^T, {\cal F})$, where $X$ is the
configuration space of a quantum system, $T$ is a time interval and ${\cal F}$
is the $\sigma$-algebra generated by the cylinder sets. Thus, it is proposed
that a quantum system can be represented as the {\it imprecise stochastic
process} $(X^T, {\cal F}, {\cal P}_\Psi)$, which is a canonical stochastic
process in which the single probability measure is replaced by a set of
measures. It is argued that this mathematical model, when used to represent
macroscopic systems, has sufficient predictive power to explain both the
results of the statistical experiments and the quasi-classical structure of the
macroscopic evolution.
