用Dirichlet分布和正交投影技术分析稳态多变量时滞系统的波动
Use of Dirichlet Distributions and Orthogonal Projection Techniques for the Fluctuation Analysis of Steady-State Multivariate Birth-Death Systems
摘要：
福克-普朗克方程的近似弱解可以作为分析生灭系统平衡涨落的有用工具，因为它们提供了介于数值模拟和精确分析论证之间的定量知识。在本文中，我们适应的一般数学形式主义被称为Ritz-Galerkin方法偏微分方程的Fokker-Planck方程与时间无关的多项式漂移和扩散系数的单纯形。然后，我们展示了如何在两个例子中，即二进制和多状态选民模型与狂热者的方法。
英文摘要：
Approximate weak solutions of the Fokker-Planck equation can 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 the present 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
