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Almost Sure Convergence of the Numerical Discretization of Stochastic Jump Diffusions (2000)

Li, C. W. ; Liu, X. Q.

Springer

Acta applicandae mathematicae 62 (2000), S. 225-244

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ISSN: 1572-9036

Keywords: jump diffusion ; Stratonovich–Taylor expansion ; exponential Lie series ; Philip Hall basis ; shuffle product ; almost sure convergence

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Based on the shuffle product expansion of exponential Lie series in terms of a Philip Hall basis for the stochastic differential equations of jump-diffusion type, we can establish Stratonovich–Taylor–Hall (STH) schemes. However, the STHr scheme converges only at order r in the mean-square sense. In order to have the almost sure Stratonovich–Taylor–Hall (ASTH) schemes, we have to include all the terms related to multiple Poissonian integrals as the moments of multiple Poissonian integrals always have lower orders of magnitudes as compared with those of multiple Brownian integrals.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1006495115904

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Efficient higher-order backward characteristics schemes for transient advection (1994)

Yu, T. S. ; Li, C. W.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 19 (1994), S. 997-1012

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ISSN: 0271-2091

Keywords: Advection ; Method of characteristics ; Finite difference ; Flux limiter ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: The use of the highest-order ((N - 1)th-order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower-order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation-free, highly accurate, efficient and more cost-effective as compared with those schemes using the highest-order Lagrangian polynomial.

Additional Material: 6 Ill.