Exact controllability of linear stochastic differential equations and related problems

Yanqing Wang; Donghui Yang; Jiongmin Yong; Zhiyong Yu

doi:10.3934/mcrf.2017011

Article Contents

2017, Volume 7, Issue 2: 305-345. Doi: 10.3934/mcrf.2017011

This issue Previous Article Nash equilibrium points of recursive nonzero-sum stochastic differential games with unbounded coefficients and related multiple\\ dimensional BSDEs Next Article

Exact controllability of linear stochastic differential equations and related problems

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2.
School of Mathematics and Statistics, School of Information Science and Engineering, Central South University, Changsha 410075, China
3.
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
4.
School of Mathematics, Shandong University, Jinan 250100, China

∗ Corresponding author: Zhiyong Yu.
∗ Corresponding author: Zhiyong Yu.

Received: January 2017

Published: August 2017

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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Abstract

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.

Keywords:

Controlled stochastic differential equation,
$L^p$-exact controllability,
observability inequality,
norm optimal control problem.

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

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References

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