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

2015/01/08 by Qi Lu, Lu, Qi
Mathematics · #60H15 #93E03 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:60H15 #msc:93E03

paper · pdf · doi:10.48550/arxiv.1501.01737

Some misprints are revised

arxiv created 2015/07/06 · arxiv updated 2015/07/07

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

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