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We generalize the concept “well-posed linear system” to stochastic linear control systems and study some basic properties of such kinds of systems. Under our generalized definition, we show the well-posedness of the stochastic heat equation and the stochastic Schrodinger equation with suitable boundary control and observation operators, respectively.

Stochastic Well-Posed Systems and Well-Posedness of Some Stochastic Partial Differential Equations with Boundary Control and Observation