Effective Approximation for a Stochastic System with Large Potential

TL;DR

This paper develops an effective approximation method for stochastic parabolic equations with large potentials in periodic media, showing that solutions can be factorized into oscillating eigenfunctions and an effective equation under spectral conditions.

Contribution

It introduces a novel approximation technique for stochastic PDEs with large potentials, leveraging spectral properties to simplify solutions.

Findings

Solution can be approximated as a product of a cell eigenfunction and an effective solution.

The approximation holds under specific spectral conditions.

Provides a framework for analyzing stochastic systems with large potentials.

Abstract

This letter is about effective approximation for a stochastic parabolic equation with a large potential in a periodic medium. Under a condition on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a solution of an effective equation.