Malliavin calculus for white noise driven parabolic SPDEs. (English) Zbl 0928.60040
For an SPDE of the form \(\partial_t X=\partial^2_t X+\psi(X)+\varphi(X)\dot{W}\) with space time white noise \(W(t,x)\), \(x\in[0,1]\), and the Neumann boundary condition, the authors use the Malliavin calculus to prove that the law of \((X(t,x_1),\ldots,X(t,x_d))\), \(0\leq x_1<\ldots<x_d\), is absolutely continuous with respect to Lebesgue measure with strictly positive density, provided the coefficients \(\psi\), \(\varphi\) are infinitely differentiable with bounded derivatives of all orders.
Reviewer: M.Capinski (Kraków)
MSC:
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
60H07 | Stochastic calculus of variations and the Malliavin calculus |
35R60 | PDEs with randomness, stochastic partial differential equations |