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Exploring the State of a Stochastic System via Stochastic Simulations: An Interesting Inversion Problem and the Health State Function

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  • Christos H. Skiadas

    (Technical University of Crete)

  • Charilaos Skiadas

    (Hanover College)

Abstract

Weexplore a method for finding the State H(t) of a Stochastic System when the first exit time or hitting time probability density function g(t) is given. The task is to find an analytic form for the state H(t) of the system thus providing a very flexible tool important in many scientific fields. The finding of this analytic form was done with the cost of an error function f(t) which we estimate in this paper by using stochastic simulations starting from the simpler linear case for H(t), then with the quadratic and higher order functions. Finally, an application to the mortality data for females in USA the year 2000 is made. We thus estimate the state of the population system or the health state of the population.

Suggested Citation

  • Christos H. Skiadas & Charilaos Skiadas, 2015. "Exploring the State of a Stochastic System via Stochastic Simulations: An Interesting Inversion Problem and the Health State Function," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 973-982, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-014-9410-y
    DOI: 10.1007/s11009-014-9410-y
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    References listed on IDEAS

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    1. J. Janssen & C. H. Skiadas, 1995. "Dynamic modelling of life table data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 35-49, March.
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    Cited by:

    1. Zhang, Xiaoqiang & Gao, Huiying & Huang, Hong-Zhong & Li, Yan-Feng & Mi, Jinhua, 2018. "Dynamic reliability modeling for system analysis under complex load," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 345-351.
    2. Christos H. Skiadas & Charilaos Skiadas, 2020. "The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1601-1611, December.

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