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2015 Fiscal Year Final Research Report

Study of accurate numerical methods and verified computation relating to stochastic differential equations

Research Project

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Project/Area Number 24760064
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Engineering fundamentals
Research InstitutionMusashino University (2015)
Future University-Hakodate (2012-2014)

Principal Investigator

TANAKA Kenichiro  武蔵野大学, 工学部, 准教授 (70610640)

Project Period (FY) 2012-04-01 – 2016-03-31
KeywordsLevy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

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Published: 2017-05-10  

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