Contributions to Applied Probability
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In the present chapter, I present mainly distributions of stopping times, which are the first epochs at which compound processes cut given boundaries. These distributions were developed for exact computations of required functionals in various applications in inventory theory, queuing theory, and more. The material discussed here is restricted to the fundamental theory, with numerical illustrations. The reader is referred to the recent book of Zacks (Sample path analysis and boundary crossing times. Lecture notes in mathematics (vol. 2203). Springer, Berlin, 2017). R-functions can be found in the Appendix.