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| Smoothness of the Functional Law Generated by a Nonlinear SPDE |
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Citation： |
Marta SANZ-SOLÉ,Paul MALLIAVIN.Smoothness of the Functional Law Generated by a Nonlinear SPDE[J].Chinese Annals of Mathematics B,2008,29(2):113~120 |
| Page view： 999
Net amount： 784 |
Authors： |
Marta SANZ-SOLé; Paul MALLIAVIN |
Foundation： |
MTM 2006-01351 from the Direcci′on General de Investigaci′on, Ministerio de Educaci′on y Ciencia, Spain. |
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| Abstract： |
The authors consider a stochastic heat equation in dimension d = 1 driven by an additive space time white noise and having a mild nonlinearity. It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE. |
Keywords： |
Stochastic heat equation, Probability law, Absolute continuity, Divergence operator, Gradient operator |
Classification： |
60H07, 60H15, 60H60 |
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