Couplings and asymptotic exponentiality of exit times (Q1806476)

The paper studies asymptotics related to exit times from a domain for small random perturbations of a dynamical system with several stable fixed points which is a partial case of the Freidlin-Wentzell setup [see \textit{M. I. Freidlin} and \textit{A. D. Wentzell}, ``Random perturbations of dynamical systems'' (1998; Zbl 0922.60006)]. The novelty of the approach is the use of coupling proposed by \textit{T. Lindvall} and \textit{L. C. G. Rogers} [Ann. Probab. 14, 860-872 (1986; Zbl 0593.60076)]. Still, the approach requires stronger assumptions and it does not eliminate the need to use parts of the Freidlin-Wentzell theory.