The Malliavin derivative, the divergence operator (Skorokhod integral), and the OrnsteinUhlenbeck operator are extended from the traditional Gaussian setting to nonlinear generalized functionals of white noise. These extensions are related to the new developments in the theory of stochastic PDEs, in particular elliptic PDEs driven by spatial white noise and quantized nonlinear equations. © 2011 Elsevier B.V. All rights reserved.
Lototsky, S. V., Rozovskii, B. L., & Seleši, D. (2012). On generalized Malliavin calculus. Stochastic Processes and Their Applications, 122(3), 808–843. https://doi.org/10.1016/j.spa.2011.11.003