Quantum stochastic differential equations and continuous measurements: unbounded coefficients

A natural formulation of the theory of quantum measurements in contmuous time is based on quantum stochastic differential equations (Hudson–Parthasarathy equations). However, such a theory was developed only in the case of Hudson–Parthasarathy equations with bounded coefficients. By using some results on Hudson–Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum contmuous measurements to cases in which unbounded operators on the system space are involved. A siginficant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses introduced in the general theory.