On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
Mytnik, Leonid ; Perkins, Edwin ; Sturm, Anja
Ann. Probab., Tome 34 (2006) no. 1, p. 1910-1959 / Harvested from Project Euclid
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We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on ℝd for d≥1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Hölder continuity of the solutions near zero is established.
Publié le : 2006-09-14
Classification:  Heat equation,  colored noise,  stochastic partial differential equation,  uniqueness,  existence,  60H15,  60K35,  60K37,  60J80,  60F05 
@article{1163517229,
     author = {Mytnik, Leonid and Perkins, Edwin and Sturm, Anja},
     title = {On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1910-1959},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163517229}
}

Mytnik, Leonid; Perkins, Edwin; Sturm, Anja. On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients. Ann. Probab., Tome 34 (2006) no. 1, pp.  1910-1959. http://gdmltest.u-ga.fr/item/1163517229/