Hitting properties of parabolic s.p.d.e.’s with reflection
Dalang, Robert C. ; Mueller, C. ; Zambotti, L.
Ann. Probab., Tome 34 (2006) no. 1, p. 1423-1450 / Harvested from Project Euclid
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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.
Publié le : 2006-07-14
Classification:  Stochastic partial differential equations,  singular coefficients,  reflecting nonlinearity,  stochastic obstacle problem,  60H15,  60J45 
@article{1158673323,
     author = {Dalang, Robert C. and Mueller, C. and Zambotti, L.},
     title = {Hitting properties of parabolic s.p.d.e.'s with reflection},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1423-1450},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1158673323}
}

Dalang, Robert C.; Mueller, C.; Zambotti, L. Hitting properties of parabolic s.p.d.e.’s with reflection. Ann. Probab., Tome 34 (2006) no. 1, pp.  1423-1450. http://gdmltest.u-ga.fr/item/1158673323/