Feynman-Kac's representation in time-space domains and sensitivity with respect to the domain
The sensitivity analysis with respect to the domain of the solution to a partial differential equation (PDE) is an old issue. The case of elliptic PDEs is well known. Previous works have tackled the parabolic case for the Laplacian in a cylindrical domain. With stochastic analysis as a tool, this note deals with more general diffusion processes and non cylindrical time-space domains. The probabilistic method makes it possible to design Monte Carlo procedures for simulation.
scientific article; zbMATH DE number 1995412
scientific article