Harnack inequalities for stochastic heat equation with locally unbounded drift

Xiuwei Yin, Guangjun Shen and Jinhong Zhang

Statistics & Probability Letters, 2020, vol. 163, issue C

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.

Keywords: Stochastic heat equation; Harnack inequality; Shift Harnack inequality (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108790

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