Hitting properties of parabolic SPDE's with reflection

• 成果类型: Article
• 署名作者: Dalang, Robert C.; Mueller, C.; Zambotti, L.
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Polytechnic University of Milan
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000792
• 发表日期: 2006
• 页码: 1423-1450
• 关键词: integration; parts

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 ut 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.