论文标题
木村方程的隐藏耗散和凸
Hidden dissipation and convexity for Kimura equations
论文作者
论文摘要
在本文中，相对于某些Wasserstein-Shahshahani最佳传输几何形状，我们建立了一个严格的梯度流量结构。这是通过首先将基本随机过程调节到非固定的来实现的，以摆脱边界上的奇异性，然后从更传统和更各种的角度研究条件$ Q $ - 过程。为此，我们完成了[Chalub等人的梯度流动公式和连续进化模型的梯度流式公式：统一的观点。 Acta App Math。，171（1），1-50]，其中仅正式识别梯度流。该方法基于耗能耗散不平等和演化变异性不平等概念。在驾驶熵功能的一定凸面上建立，我们获得了新的收缩估计值和定量的长期收敛到固定分布。
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is achieved by first conditioning the underlying stochastic process to non-fixation in order to get rid of singularities on the boundaries, and then studying the conditioned $Q$-process from a more traditional and variational point of view. In doing so we complete the work initiated in [Chalub et Al., Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective. Acta App Math., 171(1), 1-50], where the gradient flow was identified only formally. The approach is based on the Energy Dissipation Inequality and Evolution Variational Inequality notions of metric gradient flows. Building up on some convexity of the driving entropy functional, we obtain new contraction estimates and quantitative long-time convergence towards the stationary distribution.
