2015 Fiscal Year Final Research Report
Study of accurate numerical methods and verified computation relating to stochastic differential equations
| Project/Area Number |
24760064
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Engineering fundamentals
|
|---|
| Research Institution | Musashino University (2015)
Future University-Hakodate (2012-2014) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2016-03-31
|
| Keywords | Levy過程 / Kolmogorovの方程式 / 不等間隔FFT / Fractional FFT / Sinc-Gauss関数近似公式 |
|---|
| Outline of Final Research Achievements |
In this study, we proposed a numerical method for Kolmogorov's equations of Levy processes, which are popular stochastic processes. For this purpose, we designed numerical algorithms based on Fourier transform. More precisely, we accelerate the computation by the double exponential formula for Fourier transform using non-uniform FFT, proposed a numerical integration formula based on the Sinc-Gauss approximation formula, etc. By the proposed method, we succeeded in obtaining accurate numerical solutions of the Kolmogorov's equations in the time with the same order as that of FFT.
|
| Free Research Field |
数値解析学
|
