Geodesic
On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems
Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 803-819

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We prove that a single-jump unitary quantum stochastic evolution is unitarily equivalent to the Dirac boundary-value problem on the half-line in an extended space. It is shown that this solvable model can be derived from the Schrödinger boundary-value problem for a positive relativistic Hamiltonian on the half-line as the inductive ultrarelativistic limit corresponding to the input flow of Dirac particles with asymptotically infinite momenta. Thus the problem of stochastic approximation can be reduced to a quantum mechanical boundary-value problem in the extended space. The problem of microscopic time reversibility is also discussed in the paper. 
@article{MZM_2001_69_6_a0,
     author = {V. P. Belavkin},
     title = {On {Quantum} {Stochastic} {Differential} {Equations} as {Dirac} {Boundary-Value} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--819},
     publisher = {mathdoc},
     volume = {69},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a0/}
}
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V. P. Belavkin. On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems. Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 803-819. http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a0/