论文标题
由颜色噪声驱动的粘性随机热方程
Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise
论文作者
论文摘要
我们证明存在着由彩色噪声驱动的空间间隔$ [0,1] $的热方程的粘性解决方案。该过程可以解释为真实线上粘性的布朗运动的无限尺寸类似物，但是现在溶液遵循通常的随机热方程式，除了它达到零的点。在零时，解决方案没有噪音，漂移推动了它的阳性。该证明是基于一种新方法，该方法也可以应用于具有不连续系数的其他类型的SPDE。
We prove the existence of a sticky-reflected solution to the heat equation on the spatial interval $[0,1]$ driven by colored noise. The process can be interpreted as an infinite-dimensional analog of the sticky-reflected Brownian motion on the real line, but now the solution obeys the usual stochastic heat equation except points where it reaches zero. At zero the solution has no noise and a drift pushes it to stay positive. The proof is based on a new approach that can also be applied to other types of SPDEs with discontinuous coefficients.
