Entropy production of stationary diffusions on non-compact Riemannian manifolds (Q1392617)

The authors study the entropy production, for a stationary diffusion process, on a non-compact complete Riemannian manifold [for a diffusion in \({\mathbb R}^{d}\), see \textit{M. Qian} and the authors, in: Probability theory and its applications in China, Contemp. Math. 118, 255-261 (1991; Zbl 0727.60080)]. The closed form of the entropy production is given in the case of bounded Nelson's current velocity. If the Nelson's current velocity is not bounded, the authors prove that, under some conditions, the entropy production density of the reflecting diffusion process has a limit, as the reflecting domain increases to the whole manifold [see also the authors and \textit{Z. Zhao}, Probab. Theory Relat. Fields 80, No. 1, 151-167 (1988; Zbl 0631.60073)].