Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equations

TL;DR

This paper establishes Harnack inequalities, derivative formulas, and integration by parts for one-dimensional stochastic Klein-Gordon equations using coupling methods, with detailed analysis of nonlinear terms and applications.

Contribution

It introduces new Harnack inequalities and derivative formulas for stochastic Klein-Gordon equations, expanding the analytical tools for such stochastic PDEs.

Findings

Harnack inequalities derived for stochastic Klein-Gordon equations

Derivative formulas and integration by parts established

Applications demonstrated in related stochastic analysis problems

Abstract

By the coupling method, we establish the Harnack inequalities, derivative formula and Driver's integration by parts formula for the stochastic Klein-Gordon type equations in the interval. We provide a detailed discussion about the nonlinear term. Some applications are given.