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Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth–death systems

Author

Listed:
  • Filippo Palombi

    (ENEA – Italian Agency for New Technologies, Energy and Sustainable Economic Development, Via Enrico Fermi 45, 00044 – Frascati, Italy)

  • Simona Toti

    (ISTAT – Italian National Institute of Statistics, Via Cesare Balbo 16, 00184 – Rome, Italy)

Abstract

Approximate weak solutions of the Fokker–Planck equation represent a useful tool to analyze the equilibrium fluctuations of birth–death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact analytic arguments. In this paper, we adapt the general mathematical formalism known as the Ritz–Galerkin method for partial differential equations to the Fokker–Planck equation with time-independent polynomial drift and diffusion coefficients on the simplex. Then, we show how the method works in two examples, namely the binary and multi-state voter models with zealots.

Suggested Citation

  • Filippo Palombi & Simona Toti, 2015. "Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth–death systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(12), pages 1-33.
    • Handle: RePEc:wsi:ijmpcx:v:26:y:2015:i:12:n:s0129183115501399
    DOI: 10.1142/S0129183115501399
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