抛物型s.p.d.e.的命中性质。带反射的
Hitting properties of parabolic s.p.d.e.'s with reflection
摘要：
研究了一类带奇异漂移的抛物型随机偏微分方程解$u$的击中性质，该漂移使$u$不变为负值。漂移可以是反射项或非线性$cu^{-3}$，其中$c>0$。我们证明，几乎可以肯定的是，对于所有的时间$t>0$，解决方案$u_t$击中0级只有在有限数量的空间点，这明确取决于$c$。特别地，该命中数从不超过4，并且如果是$c>15/8$，则不命中等级0。
英文摘要：
We study the hitting properties of the solutions $u$ of a class of parabolic stochastic partial differential equations with singular drifts that prevent $u$ from becoming negative. The drifts can be a reflecting term or a nonlinearity $cu^{-3}$, with $c>0$. We prove that almost surely, for all time $t>0$, the solution $u_t$ hits the level 0 only at a finite number of space points, which depends explicitly on $c$. In particular, this number of hits never exceeds 4 and if $c>15/8$, then level 0 is not hit.
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