2022-01-16T19:22:30Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000401612021-03-01T21:07:15ZOn an Ergodic Property of Diffusion Semigroups on Euclidean SpaceKusuoka, Shigeo138743Liang, Song138744415ergodicitydiffusion processapplication/pdfConsider a class of uniform elliptic diffusion processes on Euclidean spaces. We estimate transition densities and their derivatives uniformly with respect to the starting points. We use these results to prove an ergodicity of ∇P_t^c (see (1.2) and Theorem 1.4) under certain conditions. This is useful in precise estimate of large deviation principles.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2003application/pdfJournal of mathematical sciences, the University of Tokyo310537553AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40161/files/jms100304.pdfeng