 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (October 2011) |
More colloquially, a first passage time in a stochastic system, is the time taken for a state variable to reach a certain value. Understanding this metric allows one to further understand the physical system under observation, and as such has 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]
- ^ Redner, S. (2001). A guide to first-passage processes. Cambridge university press.
- ^ Bachelier, L. Théorie de la spéculation. Annales scientifiques de l'École Normale Supérieure, Serie 3, Volume 17 (1900), pp. 21-86. doi : 10.24033/asens.476. http://www.numdam.org/articles/10.24033/asens.476/
- ^ Von E 1900
- ^ Smoluchowski 1915
- ^ Lundberg, F. (1903) Approximerad Framställning av Sannolikehetsfunktionen, Återförsäkering av Kollektivrisker, Almqvist & Wiksell, Uppsala.
- ^ Tweedie 1945
- ^ Tweedie 1957–1
- ^ Tweedie 1957–2
- ^ Whitmore 1970
- ^ Lancaster 1972