论文标题
达尔文的进化论是单纯上的布朗运动：随机复制器动力学的几何视角
Darwinian evolution as Brownian motion on the simplex: A geometric perspective on stochastic replicator dynamics
论文作者
论文摘要
我们证明，随机复制器动力学可以解释为在配备Aitchison几何形状的单纯形上的内在布朗运动。直接的结果，我们得出三个近似值，以Wong-Zakai的精神，Donsker的不变性原理和JKO-Scheme的精神。最后，使用Fokker-Planck方程和Wasserstein-contaction估计值，我们研究了随机复制器方程的长时间行为，作为Aitchison单纯形的非梯度漂移扩散的一个例子。
We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped the Aitchison geometry. As an immediate consequence we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Finally, using the Fokker-Planck equation and Wasserstein-contraction estimates, we study the long time behavior of the stochastic replicator equation, as an example of a non-gradient drift diffusion on the Aitchison simplex.
