# Collective behavior models with vision geometrical constraints: truncated noises and propagation of chaos

## TL;DR

This paper derives a kinetic mean-field equation for large stochastic particle systems with vision-based geometric constraints, handling discontinuous interactions and inhomogeneous noise, and constructs global solutions using Wasserstein distance.

## Contribution

It introduces a rigorous derivation of a Vlasov-Fokker-Planck type equation from stochastic systems with discontinuous kernels and geometric constraints, including global solution construction.

## Key findings

- Derived a kinetic equation from stochastic particle systems with vision constraints.
- Constructed global-in-time weak solutions for the stochastic integral inclusion system.
- Handled discontinuous kernels and inhomogeneous noise using Wasserstein distance.

## Abstract

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov-Fokker-Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.