Numerical analysis of Hamilton-Jacobi-Bellman equations and its developments

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800079
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Nakano Yumiharu 東京工業大学, 情報理工学院, 准教授 (00452409)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ハミルトン・ヤコビ・ベルマン方程式 / 確率偏微分方程式 / メッシュフリー選点法

Outline of Final Research Achievements

This study is concerned with rigorous convergence of meshfree collocation methods for nonlinear parabolic equations and linear stochastic partial differential equations, as well as with finding useful classes of basis functions and grid structures. For those equations defined on whole space, the study clarified the classes of basis functions and grid structures for which the corresponding approximation methods rigorously converge to the original equations. Also, these convergences are confined by numerical experiments. These results show that for finite horizon stochastic control problems and filtering problems for diffusion processes, the study reveals numerical methods that guarantee the rigorous convergences and need less computational time as compared with existing methods.

Free Research Field

確率制御理論