Dirichlet problem for parabolic equations on Hilbert spaces
Tom 141 / 2000
Studia Mathematica 141 (2000), 109-142 DOI: 10.4064/sm-141-2-109-142
We study a linear second order parabolic equation in an open subset of a separable Hilbert space, with the Dirichlet boundary condition. We prove that a probabilistic formula, analogous to one obtained in the finite-dimensional case, gives a solution to this equation. We also give a uniqueness result.