You arrange a 7 P.M. date at a local bistro. Your punctual date arrives at 6:55, waits until 7:05, concludes that you will not show up, and leaves. At 7:06, you saunter in – “just a few minutes” after 7 (see Cover). You assume that you arrived first and wait for your date. The wait drags on and on. “What's going on?” you think to yourself. By 9 P.M., you conclude that you were stood up, return home, and call to make amends. You explain, “I arrived around 7 and waited 2 hours! My probability of being at the bistro between 7 and 9 P.M., P(bistro, t), was nearly one! How did we miss each other?” Your date replies, “I don't care about your occupation probability. What matteredwas your first-passage probability, F(bistro, t), which was zero at 7 P.M. GOOD BYE!” Click!

The moral of this juvenile parable is that first passage underlies many stochastic processes in which the event, such as a dinner date, a chemical reaction, the firing of a neuron, or the triggering of a stock option, relies on a variable reaching a specified value for the first time. In spite of the wide applicability of first-passage phenomena (or perhaps because of it), there does not seem to be a pedagogical source on this topic. For those with a serious interest, essential information is scattered and presented at diverse technical levels. In my attempts to learn the subject, I also encountered the proverbial conundrum that a fundamental result is “well known to (the vanishingly small subset of) those who know it well.”