Summary
We prove an existence, uniqueness and unitarity theorem for quantum stochastic differential equations with unbounded coefficients which satisfy an analyticity condition on a common dense invariant domain. This result, applied to the quantum harmonic oscillator, gives a rigorous meaning to a large class of stochastic differential equations that have been considered formally in quantum probability.
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Fagnola, F. On quantum stochastic differential equations with unbounded coefficients. Probab. Th. Rel. Fields 86, 501–516 (1990). https://doi.org/10.1007/BF01198172
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DOI: https://doi.org/10.1007/BF01198172