Asymptotics of PDE in random environment by paracontrolled calculus

Tadahisa Funaki; Masato Hoshino; Sunder Sethuraman; Bin Xie

doi:10.1214/20-AIHP1129

Asymptotics of PDE in random environment by paracontrolled calculus

Tadahisa Funaki, Masato Hoshino, Sunder Sethuraman, Bin Xie

Research output: Contribution to journal › Article › peer-review

2 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 language	English (US)
Pages (from-to)	1702-1735
Number of pages	34
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1214/20-AIHP1129
State	Published - Aug 2021
Externally published	Yes

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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10.1214/20-AIHP1129

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AU - Hoshino, Masato

AU - Sethuraman, Sunder

AU - Xie, Bin

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PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - PDE in random environment

KW - Paracontrolled calculus

KW - Quasilinear stochastic PDE

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Asymptotics of PDE in random environment by paracontrolled calculus

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Keywords

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