Lifetime Data Analysis

, Volume 10, Issue 4, pp 407–423 | Cite as

Survival Models Based on the Ornstein-Uhlenbeck Process

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Abstract

When modelling survival data it may be of interest to imagine an underlying process leading up to the event in question. The Ornstein-Uhlenbeck process is a natural model to consider in a biological context because it stabilizes around some equilibrium point. This corresponds to the homeostasis often observed in biology, and also to some extent in the social sciences. First, we study the first-passage time distribution of an Ornstein-Uhlenbeck process, focussing especially on what is termed quasi-stationarity and the various shapes of the hazard rate. Next, we consider a model where the individual hazard rate is a squared function of an Ornstein-Uhlenbeck process. We extend known results on this model. The results on quasi-stationarity are relevant for recent discussions about mortality plateaus. In addition, we point out a connection to models for short-term interest rates in financial modeling.

Keywords

Cox-Ingersoll-Ross process first-passage time hazard rate mortality plateau Ornstein- Uhlenbeck process quasi-stationary distribution survival analysis 
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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of Statistics, Institute of Basic Medical SciencesUniversity of OsloOsloNorway
  2. 2.Norwegian Institute of Public HealthOsloNorway

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