On Itô's formulae for additive functionals of symmetric diffusion processes (Q2702441)

The first main result of this interesting paper is a characterization of all densities \(\rho\) for which the corresponding distorted Brownian motion \((X^\rho_t)_{t\geq 0}\) on \(\mathbb{R}^d\), i.e. the symmetric diffusion associated with the Dirichlet form NEWLINE\[NEWLINE{\mathcal E}^\rho(u,v)= {1\over 2}\int_{\mathbb{R}^d}\langle\nabla u,\nabla v\rangle \rho dxNEWLINE\]NEWLINE on \(L^2(\mathbb{R}^d, dx)\), is a semimartingale. For such \(\rho\), furthermore, a characterization of (essentially) all \(u\in C^1(\mathbb{R}^d)\) so that \(u(X^\rho_t)_{t\geq 0}\) is a semimartingale, is proved, and a representation for the bounded variation part in the Itô decomposition is derived.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00048].