【摘 要】
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We propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar Lévy processes.The method is based on the accurate numerical formul
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We propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar Lévy processes.The method is based on the accurate numerical formulas for Fourier transform proposed by Ooura.These formulas are combined with nonuniform fast Fourier transform(FFT)and fractional FFT to speed up the numerical computations.Moreover,we propose a formula for numerical indefinite integration on equispaced grids as a component of the method.The proposed integration formula is based on the sinc-Gauss sampling formula,which is a function approximation formula.This integration formula is also combined with the FFT.Therefore,all steps of the proposed method are executed using the FFT and its variants.The proposed method realizes exponential convergence and allows us to be free from some special treatments for a non-smooth initial condition and numerical time integration.
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