Abstract In this paper, using the coupling by change of measure and Krylov’s estimate, we establish the dimension-free Harnack inequalities for stochastic heat equation with Neumann boundary condition. Compared with the existing results, we only need to assume that the nonlinearity b satisfies a suitable integrability condition. As an application, we also give the distribution properties of the solution of the equation.

中文翻译：

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具有局部无界漂移的随机热方程的 Harnack 不等式

摘要 本文利用测度变化耦合和Krylov估计，建立了具有Neumann边界条件的随机热方程的无量纲Harnack不等式。与已有结果相比，我们只需要假设非线性 b 满足一个合适的可积条件。作为应用，我们还给出了方程解的分布特性。