Abstract
We consider the heat equation with a noise term, on a finite interval with periodic boundary conditions. We show how to construct coupled solutions to the equation. As applications, we prove the uniqueness of invariant measures and the triviality of bounded harmonic functions.
Citation
Carl Mueller. "Coupling and Invariant Measures for the Heat Equation with Noise." Ann. Probab. 21 (4) 2189 - 2199, October, 1993. https://doi.org/10.1214/aop/1176989016
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