An Asymptotic Comparison of Two Time-homogeneous PAM Models

TL;DR

This paper compares two interpretations of the time-homogeneous parabolic Anderson model, showing that their solutions differ by an order of e^2 as noise intensity approaches zero, with the difference being non-random.

Contribution

It provides an asymptotic analysis of the difference between Wick-Ito-Skorokhod and Stratonovich PAM solutions as noise diminishes, highlighting their convergence properties.

Findings

Solutions are real analytic in noise intensity e.

Difference between solutions is of order e^2 as e->0.

Difference is non-random in the limit.

Abstract

Both Wick-Ito-Skorokhod and Stratonovich interpretations of the parabolic Anderson model (PAM) lead to solutions that are real analytic as functions of the noise intensity e, and, in the limit e->0, the difference between the two solutions is of order e^2 and is non-random.