Asymptotics Of Pde In Random Environment By Paracontrolled Calculus
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES(2021)
Abstract
We apply the paracontrolled calculus to study the asymptotic behavior of a certain quasilinear PDE with smeared mild noise, which originally appears as the space-time scaling limit of a particle system in random environment on one dimensional discrete lattice. We establish the convergence result and show a local in time well-posedness of the limit stochastic PDE with spatial white noise. It turns out that our limit stochastic PDE does not require any renormalization. We also show a comparison theorem for the limit equation.
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Key words
Paracontrolled calculus, Quasilinear stochastic PDE, PDE in random environment
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