Error Analysis of the Feedback Controls Arising in the Stochastic Linear Quadratic Control Problems

In this work,the author proposes a discretization for stochastic linear quadratic control problems(SLQ problems)subject to stochastic differential equations.The author firstly makes temporal discretization and obtains SLQ problems governed by stochastic difference equations.Then the author derives the convergence rates for this discretization relying on stochastic differential/difference Riccati equations.Finally an algorithm is presented.Compared with the existing results relying on stochastic Pontryagin-type maximum principle,the proposed scheme avoids solving backward stochastic differential equations and/or conditional expectations.