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July 2006 Hitting properties of parabolic s.p.d.e.’s with reflection
Robert C. Dalang, C. Mueller, L. Zambotti
Ann. Probab. 34(4): 1423-1450 (July 2006). DOI: 10.1214/009117905000000792


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.


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Robert C. Dalang. C. Mueller. L. Zambotti. "Hitting properties of parabolic s.p.d.e.’s with reflection." Ann. Probab. 34 (4) 1423 - 1450, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1128.60050
MathSciNet: MR2257651
Digital Object Identifier: 10.1214/009117905000000792

Primary: 60H15
Secondary: 60J45

Keywords: reflecting nonlinearity , singular coefficients , stochastic obstacle problem , Stochastic partial differential equations

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 4 • July 2006
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