Survival models based on the Ornstein-Uhlenbeck process

Lifetime Data Analysis

Volumn 10, Issue 4, 2004, Pages 407-423

  Aalen, Odd O ^a   Gjessing, Håkon K ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b NORWEGIAN INSTITUTE OF PUBLIC HEALTH   (Norway)

Author keywords

Cox Ingersoll Ross process; First passage time; Hazard rate; Mortality plateau; Ornstein Uhlenbeck process; Quasi stationary distribution; Survival analysis

Indexed keywords

ARTICLE; COMPARATIVE STUDY; HUMAN; MORTALITY; PROPORTIONAL HAZARDS MODEL; SENSITIVITY AND SPECIFICITY; STATISTICAL MODEL; STATISTICS; SURVIVAL;

HUMANS; MODELS, STATISTICAL; MORTALITY; PROPORTIONAL HAZARDS MODELS; SENSITIVITY AND SPECIFICITY; STOCHASTIC PROCESSES; SURVIVAL ANALYSIS;

EID: 14844315957     PISSN: 13807870     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10985-004-4775-9     Document Type: Conference Paper

References (29)

1. O.O. Aalen H.K. Gjessing 2001 Understanding the shape of the hazard rate Statistical Science 16 1 22
2. O.O. Aalen H.K. Gjessing 2003 A look behind survival data: Underlying processes and quasi-stationarity B.H. Lindqvist K.A. Doksum Mathematical and Statistical Methods in Reliability World Scientific Publishing Singapore 221 234
3. M. Abramowitz I.A. Stegun 1964 Handbook of Mathematical Functions Dover Publications New York
4. M. Baxter A. Rennie 1997 Financial Calculus. An Introduction to Derivative pricing Cambridge University Press New York
5. J.C. Cox J.E. Ingersoll S.A. Ross 1985 A theory of the term structure of interest rates Econometrica 53 385 407
6. H.K. Gjessing O.O. Aalen N.L. Hjort 2003 Frailty models based on Lévy processes Advances in Applied Probability 35 532 550
7. S. Karlin H.M. Taylor 1981 A Second Course in Stochastic Processes Academic Press New York
8. J. Keilson 1966 A limit theorem for passage times in ergodic regenerative processes Annals of Mathematical Statistics 37 866 870
9. M.-L.T. Lee V. DeGruttola D. Schoenfeld 2000 A model for markers and latent health status Journal of the Royal Statistical Society B 62 747 762
10. N.N. Lebedev 1972 Special Functions and Their Applications Dover Publications New York
11. M. Lladser J. San Martin 2000 Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process Journal of Applied Probability 37 511 520
12. K.G. Manton E. Stallard 1988 Chronic Disease Modelling Charles Griffin Company Limited London
13. M. Musiela M. Rutkowski 1997 Martingale Methods in Financial Modelling Springer-Verlag New York
14. L.E. Myers 1981 Survival functions induced by stochastic covariate processes Journal of Applied Probability 18 523 529
15. B. Øksendal 1998 Stochastic differential equations Springer-Verlag Berlin
16. J. Paulsen H.K. Gjessing 1997 Ruin theory with stochastic return on investments Advances in Applied Probability 29 965 985
17. L.M. Ricciardi S. Sato 1988 First-passage-time density and moments for the Ornstein-Uhlenbeck process Journal of Applied Probability 25 43 57
18. G. Samorodnitsky 2002 Long Range Dependence, Heavy Tails and Rare Events, Lecture Notes Maphysto Centre for Mathematical Physics and Stochastics Aarhus
19. N.D. Singpurwalla 1995 Survival in dynamic environments Statistical Science 10 86 103
20. D. Steinsaltz S.N. Evans 2004 Markov mortality models: Implications of quasistationarity and varying initial distributions Theoretical Population Biology 65 319 337
21. D. Steinsaltz S.N. Evans 2003 Quasistationary distributions for one-dimensional diffusions with killing'', Technical report, Department of Statistics University of California Berkeley
22. M.L. Wenocur 1990 Ornstein-Uhlenbeck processes with quadratic killing Journal of Applied Probability 27 707 712
23. S. Wolfram, The Mathematica book, 4th edition, Wolfram Media/Cambridge University Press, 1999.
24. S. Wolfram (2004a). http://functions.wolfram.com/07.01.06.0009.01.
25. S. Wolfram (2004b). http://functions.wolfram.com/07.20.06.0009.01.
26. M.A. Woodbury K.G. Manton 1977 A random walk model of human mortality and aging Theoretical Population Biology 11 37 48
27. A.I. Yashin 1985 Dynamics in survival analysis: conditional Gaussian property versus Cameron-Martin formula N.V. Krylov R.S. Liptser A.A. Novikov Statistics and control of stochastic processes Springer New York 466 475
28. A.I. Yashin K.G. Manton 1997 Effects of unobserved and partially observed covariate processes on system failure: A review of models and estimation strategies Statistical Science 12 20 34
29. A. I. Yashin and J. W. Vaupel, ''Measurement and estimation in heterogeneous populations,'' in Lecture Notes in Biomathematics 65: Immunology and Epidemiology (Hoffman GW and Hraba T, eds.) pp. 198-206, 1986.