Meshfree Approximation for Stochastic Optimal Control Problems

• 作者: Hui Sun Feng Bao
• 来源期刊: 数学研究通讯
• 年，卷（期）: 2021,（3）
• 页码范围: 386-418
• 页数: 33页
• 语种: 英文
• DOI: 10.4208/cmr.2021-0022

摘要

In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion is to extend the existing gradient projection method to moderate high-dimensional space.The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework,and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach.We also present several numerical experiments to validate the theoretical re-sults of our approach and demonstrate the performance meshfree approxima-tion in solving stochastic optimal control problems.