Semimartingale attractors for generalized Allen–Cahn SPDEs driven by space–time white noise

Weighted Stochastic Sobolev Spaces and B

Weighted Stochastic Sobolev Spaces and Bilinear SPDEs Driven by Space–Time White Noise

✍ David Nualart; Boris Rozovskii 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 426 KB

In this paper we develop basic elements of Malliavin calculus on a weighted L 2 (0). This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller than the space of Hida distributions while large enough to accommodate solutions of bilinear stochastic PDEs.