  The relationship between discontinuous and continuous stochastic processes in
Hilbert space is investigated. It is shown that for any continuos process there
is a parent discontinuous process, that becomes the continuous one in the
proper infinite frequency limit. From the point of view of solving the quantum
measurement problem, what really matters is the choice of the set of operators
whose value distributions are made sharp. In particular, the key role of
position sharping is emphasized.
