Smoothness of the functional law generated by a nonlinear SPDE

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

References

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