The fluctuation behaviour of the stochastic point vortex model with common noise

TL;DR

This paper investigates the fluctuation behavior of a stochastic point vortex model influenced by common noise, demonstrating convergence to a linear stochastic evolution equation and the conditional McKean Vlasov equation.

Contribution

It establishes the strong convergence of the stochastic point vortex model with common noise to the conditional McKean Vlasov equation using martingale and localization methods.

Findings

Fluctuation processes converge in distribution to a linear stochastic evolution equation.

Proves strong convergence from the vortex model to the conditional McKean Vlasov equation.

Utilizes martingale method combined with localization argument.

Abstract

This article studies the fluctuation behaviour of the stochastic point vortex model with common noise. Using the martingale method combined with a localization argument, we prove that the sequence of fluctuation processes converges in distribution to the unique probabilistically strong solution of a linear stochastic evolution equation. In particular, we establish the strong convergence from the stochastic point vortex model with common noise to the conditional McKean Vlasov equation.