First-hitting-time model

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In statistics, first-hitting-time models are simplified models that estimate the amount of time that passes before some random or stochastic process crosses a barrier, boundary or reaches a specified state, termed the first hitting time, or the first passage time. Accurate models give insight into the physical system under observation, and have been the topic of research in very diverse fields, from economics to ecology.^[1]

The idea that a first hitting time of a stochastic process might describe the time to occurrence of an event has a long history, starting with an interest in the first passage time of Wiener diffusion processes in economics and then in physics in the early 1900s.^[2][3][4] Modeling the probability of financial ruin as a first passage time was an early application in the field of insurance.^[5] An interest in the mathematical properties of first-hitting-times and statistical models and methods for analysis of survival data appeared steadily between the middle and end of the 20th century.^{[6][7][8][9][10]}

First-hitting-time models are a sub-class of survival models.