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Exact controllability of linear stochastic differential equations and related problems

  • ∗ Corresponding author: Zhiyong Yu.

    ∗ Corresponding author: Zhiyong Yu.
the National Natural Science Foundation of China (11471192, 11371375, 11526167), the Fundamental Research Funds for the Central Universities (SWU113038, XDJK2014C076), the Nature Science Foundation of Shandong Province (JQ201401), the Natural Science Foundation of CQCSTC (2015jcyjA00017), China Postdoctoral Science Foundation and Central South University Postdoctoral Science Foundation, and NSF Grant DMS-1406776.
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  • A notion of $L^p$ -exact controllability is introduced for linear controlled (forward) stochastic differential equations with random coefficients. Several sufficient conditions are established for such kind of exact controllability. Further, it is proved that the $L^p$ -exact controllability, the validity of an observability inequality for the adjoint equation, the solvability of an optimization problem, and the solvability of an $L^p$ -type norm optimal control problem are all equivalent.

    Mathematics Subject Classification: Primary: 93B05, 93E20; Secondary: 60H10.

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