In this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions \(d=2,3\). Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

中文翻译：

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随机Keller-Segel方程的微观推导和适定性

在本文中，我们提出并研究了Keller-Segel（KS）类型的随机聚集-扩散方程，用于对尺寸\（d = 2,3 \）中的趋化性进行建模。与仅允许特异噪声的经典确定性KS系统不同，随机KS方程是从受特异噪声和普通噪声共同作用的粒子系统中得出的。既解决了随机KS方程解的唯一性，又解决了均场极限结果。