# The microscopic derivation and well-posedness of the stochastic Keller-Segel equation

## TL;DR

This paper derives a stochastic Keller-Segel equation from particle systems with combined noises, establishing its well-posedness and connecting it to the classical model.

## Contribution

It provides a microscopic derivation and rigorous analysis of the stochastic Keller-Segel equation, including existence and mean-field limit results.

## Key findings

- Proves unique existence of solutions to the stochastic KS equation.
- Establishes the mean-field limit from particle systems with combined noises.
- Extends classical Keller-Segel models to stochastic settings.

## Abstract

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.