Malliavin calculus for white noise driven parabolic SPDEs
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.
stochastic partial differential equations
scientific article; zbMATH DE number 1241116