Probability Approximations via the Poisson Clumping Heuristic: An Update

This is a collection of corrections and additions to the book, and references to subsequent work. Perhaps the main development since going to press has been continued work by Barbour et al and by Arratia et al, referenced below, on using Stein's method to get explicit bounds for Poisson approximation. However, I have not yet seen any convincing implementation of the Compound Poisson case. Also of interest is a new book by Berman 14] which collects together his extensive research results on extremes and sojourns: the Gaussian case is emphasized, but also discussed are diiusions, birth-and-death processes and d-dimensional orthogonally invariant processes.