We associate with a strong Markov process $(X_t)$ and a Borel set $B$ an "exit system." This system provides the structure of the excursions from $B$ of the process $(X_t)$ and gives a new approach to the recent results of Getoor and Sharpe on last exit decompositions and last exit distributions.
"Exit Systems." Ann. Probab. 3 (3) 399 - 411, June, 1975. https://doi.org/10.1214/aop/1176996348