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      Stochastic Well-posed Systems and Well-posedness of Some Stochastic Partial Differential Equations with Boundary Control and Observation

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          Abstract

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

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          Admissibility of Unbounded Control Operators

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            Admissible observation operators for linear semigroups

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              Well-posed systems—The LTI case and beyond

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                Author and article information

                Journal
                2015-01-08
                2015-07-06
                Article
                1501.01737
                9ca275c9-c306-4494-9dcb-f0d8456396d1

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                93E03, 60H15
                Some misprints are revised
                math.OC

                Numerical methods
                Numerical methods

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