Rarity and exponentiality: an extension of Keilson's theorem, with applications
Rudolf Grübel, Marcus Carlsson Reich · Journal of Applied Probability · 2005
We generalize a theorem due to Keilson on the approximate exponentiality of waiting times for rare events in regenerative processes. We use the result to investigate the limit distribution for a family of first entrance times in a sequence of Ehrenfest urn models. As a second application, we consider approximate pattern matching, a problem arising in molecular biology and other areas.