Study of accurate numerical methods and verified computation relating to stochastic differential equations
| Project/Area Number |
24760064
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Engineering fundamentals
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| Research Institution | Musashino University (2015)
Future University-Hakodate (2012-2014) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Levy過程 / Kolmogorovの方程式 / 不等間隔FFT / Fractional FFT / Sinc-Gauss関数近似公式 / 分布関数 / Fourier変換 / Kolmogorvの前進方程式 / Sinc-Gaussサンプリング公式 / Kolmogorovの前進方程式 / 二重指数関数型（DE）公式 / DE-Sinc法 / Kolmogorovの前進/後退方程式 |
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| 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.
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Report
(5 results)
Research Products
(23 results)
