# American Institute of Mathematical Sciences

June  2017, 7(2): 305-345. doi: 10.3934/mcrf.2017011

## 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.

Received  January 2017 Published  April 2017

Fund Project: 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.

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.

Citation: Yanqing Wang, Donghui Yang, Jiongmin Yong, Zhiyong Yu. Exact controllability of linear stochastic differential equations and related problems. Mathematical Control & Related Fields, 2017, 7 (2) : 305-345. doi: 10.3934/mcrf.2017011
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show all references

##### References:
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