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Search for the symmetry of the Fokker-Planck equation

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  • An, Ing
  • Chen, Shi
  • Guo, Han-ying

Abstract

It is shown that the Fokker-Planck equations with linear drift γx and nonlinear drift γx + δx, i.e. the Rayleigh process, have exact symmetries on their own solution manifolds, the sl(2, R) ⊗ Weyl algebra and the sl(2, R) ⊗ I, respectively. The symmetries of these two types of processes for 1 + 2-dimensional cases are explicitly found out too.

Suggested Citation

  • An, Ing & Chen, Shi & Guo, Han-ying, 1984. "Search for the symmetry of the Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 520-528.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:3:p:520-528
    DOI: 10.1016/0378-4371(84)90190-0
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    References listed on IDEAS

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    1. Ding, E-Jiang, 1983. "Asymptotic properties of the Markovian master equations for multi-stationary systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 317-326.
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    Cited by:

    1. Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
    2. P. Lencastre & F. Raischel & P. G. Lind, 2014. "The effect of the number of states on the validity of credit ratings," Papers 1409.2661, arXiv.org.
    3. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    4. Robin Nicole & Aleksandra Alori'c & Peter Sollich, 2020. "Fragmentation in trader preferences among multiple markets: Market coexistence versus single market dominance," Papers 2012.04103, arXiv.org, revised Aug 2021.
    5. Tushar Vaidya & Thiparat Chotibut & Georgios Piliouras, 2019. "Broken Detailed Balance and Non-Equilibrium Dynamics in Noisy Social Learning Models," Papers 1906.11481, arXiv.org, revised May 2020.

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