Asymptotics of PDE in random environment by paracontrolled calculus

Tadahisa Funaki, Masato Hoshino, Sunder Sethuraman, Bin Xie

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1702-1735
Number of pages34
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume57
Issue number3
DOIs
StatePublished - Aug 2021

Keywords

  • PDE in random environment
  • Paracontrolled calculus
  • Quasilinear stochastic PDE

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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