  In this article we look at stochastic processes with uncertain parameters,
and consider different ways in which information is obtained when carrying out
observations. For example we focus on the case of a the random evolution of a
traded financial asset price with uncertain volatility. The quantum approach
presented, allows us to encode different volatility levels in a state acting on
a Hilbert space. We consider different means of defining projective
measurements in order to track the evolution of a traded market price, and
discuss the results of different Monte-Carlo simulations.
