A remark on a result of Xia Chen

TL;DR

This paper extends Xia Chen's results on the parabolic Anderson model by providing a method to compute Lyapunov exponents for all moments of order p ≥ 2, where p is any real number.

Contribution

It introduces an extension of Xia Chen's work to include all real moments p ≥ 2 for the model's Lyapunov exponents.

Findings

Extended the calculation of Lyapunov exponents to all real moments p ≥ 2

Provided a generalized approach for the parabolic Anderson model with fractional Gaussian noise

Enhanced understanding of the model's moment behavior across a continuous range of p

Abstract

We consider the parabolic Anderson model which is driven by a Gaussian noise fractional in time and having certain scaling property in the spatial variables. Recently, Xia Chen has obtained exact Lyapunov exponent for all moments of positive integer orders. In this note, we explain how to extend Xia Chen's result for all moments of order $p$, where $p$ is any real number at least 2.