REFERENCES

[1] O. O. Aalen, H. K. Gjessing, Survival models based on the OrnsteinUhlenbeck

process, Lifetime Data Analysis, 10, No. 4 (2004), 407-423.

[2] H. Akaike, A new look at the statistical model identification, IEEE Transactions

on Automatic Control, 19 (1974), 716-723.

[3] I. Akushevich, L. Akushevich, K. Manton, A. Yashin, Stochastic Pro-

cess Model of Mortality and Aging: Application to Longitudinal Data,

Nonlinear Phenomena in Complex Systems, 6 (2003), 515-523.

[4] E. J. Allen, Modeling With Itˆo Stochastic Differential Equations, Springer,

Dordrecht, 2007.

[5] E. Allen, Stochastic differential equation models for the wear of coins in

circulation, Tribology Letters, 64 (2016), 1-8.

[6] E. Allen, Bounds on mean exit time for purely time-dependent drift and

diffusion, Communications in Applied Analysis (2017), to appear.

[7] L. J. S. Allen, An Introduction to Stochastic Processes with Applications

to Biology, Second Edition, CRC Press, Chapman & Hall Publishers,

Boca Raton, 2010.

[8] E. Arias, United States Life Tables, 2010, National Vital Statistics Reports

63 (2014), 1-63.

[9] B. Benjamin, The span of life, Journal of the Institute of Actuaries, 109

(1982), 319-357.

[10] J. R. Carey, P. Liedo, D. Orozco, J. W. Vaupel, Slowing of mortality rates

at older ages in large medfly cohorts, Science, 258 (1992), 457-461.

[11] B. H. Chen, et al., DNA methylation-based measures of biological age:

meta-analysis predicting time to death, Aging, 8 (2016), 1844-1865.

[12] E. S. Deevey, Jr. , Life Tables for Natural Populations of Animals, The

Quarterly Review of Biology 22 (1947), 283-314.

[13] Y. Deng, A. Barros, A. Grall, Residual useful life estimation based

on a time-dependent Ornstein-Uhlenbeck process, Chemical Engineering

Transactions, 33 (2013), 325-330.

[14] Y. Deng, Degradation modeling based on a time-dependent OrnsteinUhlenbeck

process and prognosis of system failures, Dissertation, University

of Technology of Troyes, 2015.

[15] C. E. Finch, M. C. Pike, Maximum Life Span Predictions From the Gompertz

Mortality Model, Journal of Gerontology: Biological Sciences, 51A

(1996), B183-B194.

[16] M. Finkelstein, On engineering reliability concepts and biological aging,

Reliability: Theory & Applications, 3, No. 10 (2008), 37-47.

[17] J. L. Folks, R. S. Chhikara, The inverse Gaussian distribution and its

statistical application – a review, Journal of the Royal Statistical Society:

Series B 40 (1978), 263-289.

[18] T. C. Gard, Introduction to Stochastic Differential Equations, Marcel

Decker, New York, 1987.

[19] N. S. Gavrilova, L. A. Gavrilov, Ageing and Longevity: Mortality Laws

and Mortality Forecasts for Ageing Populations, Demografie, 53 (2011),

109-128.

[20] L. A. Gavrilov, N. S. Gavrilova, The Reliability Theory of Aging and

Longevity, Journal of Theoretical Biology, 213 (2001), 527-545.

[21] S. Kim, S. M. Jazwinski, Quantitative measures of healthy aging and

biological age, Healthy Aging Research, 4 (2015), 1-14.

[22] P. E. Kloeden, E. Platen, H. Schurz, Numerical Solution of SDE Through

Computer Experiments, Springer, Berlin, 1994.

[23] A. G. Ladde, G. S. Ladde, An Introduction to Differential Equations:

Stochastic Modeling, Methods and Analysis, Volume 2, World Scientific

Publishing Company, Singapore, 2013.

[24] R. B. McDonald, Biology of Aging, Garland Science, New York, 2013.

[25] A. Molini, P. Talkner, G. G. Katul, A. Porporato, First passage time

statistics of Brownian motion with purely time dependent drift and diffusion,

Physica A: Statistical Mechanics and its Applications 390 (2011),

1841-1852.

[26] O. Murie, The Wolves of Mount Mckinley, U.S. Department of Interior,

United States Government Printing Office, Washington D.C., 1944.

[27] S. Nath, A, Rai, Study of life table of Ceracris nigricornis laeta (Orthoptera:

acrididae) in laboratory conditions, Romanian Journal of Biology

- Zoology, 55 (2010) 159-165.

[28] J. A. Nelder and R. Mead, Simplex method for function minimization,

The Computer Journal, 7 (1965), 308-313.

[29] L. Partridge and M. Farquhar, Sexual activity reduces lifespan of male

fruitflies, Nature, 294 (1981), 580-582.

[30] J. B. Roberts, First-passage probabilities for randomly excited systems:

diffusion methods, Probabilistic Engineering Mechanics, 1 (1986), 66-81.

[31] W. C. Sanderson, S. Scherbov, Measuring the Speed of Aging across Population

Subgroups, PLoS ONE, 9 (2014) 1-4.

[32] C. H. Skiadas, C. Skiadas, Comparing the Gompertz-Type Models with

a First Passage Time Density, in: Advances in Data Analysis, (Ed: C. H.

Skiadas), Springer/Birkhauser, Boston, 2010.

[33] C. Skiadas and C. H. Skiadas, Development, simulation, and application

of first-exit-time densities to life table data, Communications in Statistics

- Theory and Methods, 39 (2010), 444-451.

[34] D. Strauss and R. K. Eyman, Mortality of people with mental retardation

in California with Down syndrome, 1986-1991, American Journal of

Mental Retardation 100 (1996), 643-653.

[35] L. Sun, X. Gu, P. Song, Accelerated Degradation Process Analysis Based

on the Nonlinear Wiener Process with Covariates and Random Effects,

Mathematical Problems in Engineering 2016 (2016), 1-13.

[36] D. Weber, Differences in physical aging measured by walking speed: evidence

from the English Longitudinal Study of Ageing, BMC Geriatrics,

16:31 (2016).

[37] G. A. Whitmore, F. Schenkelberg, Modelling accelerated degradation

data using Wiener diffusion with a time scale transformation, Lifetime

Data Analysis, 3 (1997), 27-45.

[38] Z. Yang, Maximum likelihood predictive densities for the inverse Gaussian

distribution with applications to reliability and lifetime predictions,

Microelectronics Reliability, 39 (1999), 1413-1421.

[39] A. I. Yashin, K. G. Arbeev, I. Akushevich, A. Kulminski, L. Akushevich,

S. V. Ukraintseva, Stochastic model for analysis of longitudinal data on

aging and mortality, Mathematical Biosciences, 208 (2007), 538-551.

[40] Z.-S. Ye, M. Xie, Stochastic modelling and analysis of degradation for

highly reliable products, Applied Stochastic Models in Business and Industry,

31 (2015), 16-32.