Research on explicit numerical methods for high-dimensional stochastic differential equations

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K05369
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: Komori Yoshio 九州工業大学, 大学院情報工学研究院, 准教授 (20285430)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Keywords: 陽的解法 / 確率微分方程式 / ルンゲ・クッタ・チェビシェフ / 確率遅延微分方程式 / Exponential Runge-Kutta

Outline of Final Research Achievements

In order to understand phenomena in many fields such as Biochemistry, Physics and Finance, we can utilize mathematical models and they are helpful for us to predict how a phenomenon evolves as time goes. The mathematical models are usually described by differential equations such as ordinary differential equations (ODEs). In the present research project, we have derived new numerical methods for stochastic differential equations (SDEs), which are ODEs with noise terms. They will help us to investigate the time evolutions of phenomena described by SDEs.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

確率偏微分方程式を空間方向に離散化すると高い次元のSDE が現れる. 一般的に,これは数値的に解きにくいstiff な問題になる. 本研究課題に挙げた数値解法は, それを高精度で高速に解くことができる.
数理解析に対する要求の高まりとともに, 確率的な振る舞いを考慮した数理モデルが今後様々な分野に広がることが予想される. したがって，本研究課題の成果は将来的に非常に広範な分野に影響を及ぼすと考えられる.