  We prove that a single-jump quantum stochastic unitary evolution is
equivalent to a Dirac boundary value problem on the half line in an extra
dimension. This amounts to the equivalence of the quantum measurement
boundary-value problem in infinite number particles space to the stochastic
calculus in Fock space. It is shown that this exactly solvable model can be
obtained from a Schroedinger boundary value problem for a positive relativistic
Hamiltonian in the half-line as the inductive ultra relativistic limit,
correspondent to the input flow of Dirac particles with asymptotically infinite
momenta. Thus the stochastic limit can be interpreted in terms of quantum
stochastic scheme for time-continuous non-demolition observation. The question
of microscopic time reversibility is also studied for this paper.
