从个体基模型到一般随机反应扩散方程

中文摘要 AI 辅助

在本文中，我们针对一大类一维随机反应扩散方程，构造了一列具有空间结构的个体基模型，其重标度经验过程收敛于该方程的解。本文旨在表明，只要一个合理的个体基模型的重标度一步均值和方差收敛于具有漂移项 $b(x)x(1-x)+\theta^+(1-x)-\theta^-x$ 和噪声系数 $\sqrt{\sigma(x)x(1-x)}$ 的随机微分方程（SDE）的相应量，并且在一定的矩条件下，还存在一个相应的多岛屿模型，该模型由每个岛屿上独立同分布的个体基模型副本组成，选择与突变按扩散时间尺度缩放，并通过迁移耦合，只要该随机偏微分方程（SPDE）在分布意义下唯一，则该多岛屿模型收敛于具有拉普拉斯算子以及相同漂移和噪声系数的SPDE。

英文摘要

In this article, we construct, for a broad class of one-dimensional stochastic reaction-diffusion equations, a sequence of spatially-structured individual-based models whose rescaled empirical processes converge to the solution of the equation. The purpose of this article is to show that, whenever the rescaled one-step mean and variance of a reasonable individual-based model converge to those of an SDE with drift $b(x)x(1-x)+θ^+(1-x)-θ^-x$ and noise coefficient $\sqrt{σ(x)x(1-x)}$, under certain moment conditions there also exists a corresponding multi-island model, composed of independent and identically distributed copies of the individual-based model on each island, with selection and mutation scaled to the diffusive time scale, coupled through migration, which converges to an SPDE with a Laplacian plus the same drift and noise coefficients, provided this SPDE is unique in law.

发表机构

• Arizona State University（亚利桑那州立大学）

机构由 AI 辅助整理，请以论文原文为准。