  We propose a new model for a measurement of a characteristic of a microscopic
quantum state by a large system that selects stochastically the different
eigenstates with appropriate quantum weights. Unlike previous works which
formulate a modified Schr\"odinger equation or an explicit modified
Hamiltonian, or more complicated mechanisms for reduction and decoherence to
introduce transition to classical stochasticity, we propose the novel use of
couplings to the environment, and random walks in the product Hilbert space of
the combined system, with first passage stopping rules, which seem intuitively
simple, as quantum weights and related stochasticity is a commonality that must
be preserved under the widest range of applications, independent of the
measured quantity and the specific properties of the measuring device.
