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

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 Schrödinger equation with suitable boundary control and observation operators, respectively.

preprint2015arXivOpen access
Qi Lu
math.OC
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Qi Lu

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