The effect of noise intensity on stochastic parabolic equations

TL;DR

This paper investigates how varying noise intensity influences the energy solutions of stochastic parabolic equations, providing new insights and simplified methods to determine excitation indices.

Contribution

It introduces a straightforward approach to analyze the effect of noise on energy solutions and improves upon existing results in the literature.

Findings

Derived excitation indices for energy solutions at finite times

Presented a simplified method for analyzing noise effects

Enhanced understanding of noise impact on stochastic parabolic equations

Abstract

In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising It\^o's formula and the energy estimate method, we obtain the excitation indices of the energy solutions $u$ at any finite time $t$. Furthermore, we improve certain existing results in the literature by presenting a comparably simple method to show those existing results.