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

Qi Lu

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arXiv · 1501.01737

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

Qi Lu

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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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Qi Lu. 2015-01-08. Stochastic Well-posed Systems and Well-posedness of Some Stochastic Partial Differential Equations with Boundary Control and Observation. https://arxiv.org/abs/1501.01737

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