Similarity transformations of hypersurfaces

Wong, Yuen-Fat

doi:10.1090/s0002-9939-1964-0161279-5

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A the Repulsive Wong Process1

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2000

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Cited by 2 publications

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“…The repulsive Wong process is Markovian due to the deriving Gaussian white noise term. Its transition probability density is governed by the Fokker-Planck equation of the form [38][39][40] ∂f (x, t) ∂t…”

Section: A the Repulsive Wong Processmentioning

confidence: 99%

A unified approach for the solution of the Fokker-Planck equation

Wei

2000

J. Phys. A: Math. Gen.

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This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genuine nonlinear model, are employed to illustrate the robustness and to test accuracy of the present approach for the solution of the Fokker-Planck equation via a timedependent method. An additional example, the incompressible Euler equation, is used to further validate the present approach for more difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.

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Section: A the Repulsive Wong Processmentioning

confidence: 99%