随机偏微分方程的概率Harnack不等式与严格正性
A probabilistic Harnack inequality and strict positivity of stochastic partial differential equations
摘要：
在一般条件下，证明了一类随机偏微分方程d_tu = div（A \nabla u）+ f（t，x，u;w）+ g_i（t，x，u;w）\dot{w}^i_t非负解的先验概率Harnack不等式.我们还将证明，上述方程的解将几乎必然严格正，如果初始条件是非负的，而不是同零。
英文摘要：
Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form d_tu = div (A\nabla u) + f (t, x, u;w) + g_i(t, x, u;w)\dot{w}^i_t. We will also show that the solution of the above equation will be almost surely strictly positive if the initial condition is non-negative and not identically vanishing.
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