2022-11-29T13:29:11Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/690652022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Weak convergence on the first exit time of randomly perturbed dynamical systems with a repulsive equilibrium pointMikami, T.410We show that the first exit times of small random perturbations of dynamical systems from a bounded domain D(c Rd) weakly converge to the explosion time of an explosive diffusion process and that the mean first exit times converge to the mean explosion time, as random perturbations disappear, when they are appropriately scaled. We consider the case when D contains only one equilibrium point o of dynamical systems and when o is polynomially unstabe and is repulsive.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69065info:doi/10.14943/83461https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69065/1/pre314.pdfHokkaido University Preprint Series in Mathematics3141201995-11-01engpublisher