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. © 2015 World Scientific Publishing Company.

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

Palombi, F.
2015

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. © 2015 World Scientific Publishing Company.
Fokker-Planck equation;voter models;Ritz-Galerkin method;Birth-death models
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12079/2154
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