6 papers · 1 filter
On the role of positivity preservation for high order approximations of the Dean--Kawasaki equation
Ana DamnjanoviÄ, Ana Djurdjevac, Nicolas Perkowski
We study a spectral regularization of the Dean--Kawasaki equation and quantify how the failure of positivity preservation affects its weak approximation of the empirical measure of…
Surface Dean--Kawasaki equations
John Bell, Ana Djurdjevac, Nicolas Perkowski
We consider stochastic particle dynamics on hypersurfaces represented in Monge gauge parametrization. Starting from the underlying Langevin system, we derive the surface Dean-Kawas…
A Rough Functional Breuer-Major Theorem
Henri Elad Altman, Tom Klose, Nicolas Perkowski
We extend the functional Breuer-Major theorem by Nourdin and Nualart (2020) to the space of rough paths. The proof of tightness combines the multiplication formula for iterated Mal…
Renormalization destroys a finite time bifurcation in the equation
Alexandra Blessing, Nicolas Perkowski, Chara Zhu
We study the singular equation at a pitchfork bifurcation of the underlying deterministic dynamics. To this aim, we linearize the SPDE along its stationary solution and sh…
Coming up from for KPZ via stochastic control
Nicolas Perkowski, Carlos Villanueva Mariz
We derive a lower bound, independent of the initial condition, for the solution of the KPZ equation on the torus through its representation as the value function of a (conditional)…
Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions
Ana Djurdjevac, Xiaohao Ji, Nicolas Perkowski
We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô noise for particle systems with mean-field interactions both on the drift…