First-hitting-time model

Events are often triggered when a stochastic or random process first encounters a threshold. The threshold can be a barrier, boundary or specified state of a system. The amount of time required for a stochastic process, starting from some initial state, to encounter a threshold for the first time is referred to variously as a first hitting time. In statistics, first-hitting-time models are a sub-class of survival models. The first hitting time, also called first passage time, of the barrier set with respect to an instance of a stochastic process is the time until the stochastic process first enters .