Haydn, Lacroix and Vaienti (2005 Ann. Probab. 33 2043–50) proved that, for a given ergodic map, the entry time distribution converges in the small target limit, if and only if the corresponding return time distribution converges. The present note explains how entry and return times can be interpreted in terms of stationary point processes and their Palm distribution. This permits a generalization of the results by Haydn et al to non-ergodic maps and continuous-time dynamical systems.
- return times
- Kac formula
- palm distribution
- point process Mathematics Subject Classification numbers: 37A10, 60G55