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Maximum-entropy approach with higher moments for solving Fokker–Planck equation

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  • El-Wakil, S.A.
  • Abulwafa, E.M.
  • Abdou, M.A.
  • Elhanbaly, A.

Abstract

The maximum-entropy method with higher number of moments is used to solve the Fokker–Planck equation. An adopted Newton method is used to iterate the maximum entropy set of equations. The method is used to calculate the probability density function of the Fokker–Planck equation. The calculations are carried out for three examples. (1) The bistable systems of double well potential that is used in many problems related to the fluctuation and relaxation processes in far from equilibrium systems. (2) The Malthus–Verhulst model, which is used to study the evolution of the number of individuals of an ecological species and the evolution of the intensity of the laser light. (3) The Black–Scholes equation used in financial market option pricing. Although the maximum-entropy approach has several advantages, it is not convergent at large times and so cannot be used to calculate the steady state solution.

Suggested Citation

  • El-Wakil, S.A. & Abulwafa, E.M. & Abdou, M.A. & Elhanbaly, A., 2002. "Maximum-entropy approach with higher moments for solving Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 480-492.
    • Handle: RePEc:eee:phsmap:v:315:y:2002:i:3:p:480-492
    DOI: 10.1016/S0378-4371(02)01001-4
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    References listed on IDEAS

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    1. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    2. Ma, Ben Kun & Liu, Shao Jun, 1992. "Perturbation series solution of the Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(1), pages 148-158.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. So, F. & Liu, K.L., 2000. "A study of the Fokker–Planck equation of bistable systems by the method of state-dependent diagonalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(3), pages 335-348.
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    Cited by:

    1. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

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