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Range reliability in random walks

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  • Pierre Vallois
  • Charles Tapiero

Abstract

This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is denned as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic. Copyright Physica-Verlag 1997

Suggested Citation

  • Pierre Vallois & Charles Tapiero, 1997. "Range reliability in random walks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 325-345, October.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:3:p:325-345
    DOI: 10.1007/BF01194783
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    References listed on IDEAS

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    1. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
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    Cited by:

    1. Tapiero, Charles S. & Vallois, Pierre, 2016. "Fractional randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1161-1177.
    2. Vallois, Pierre & Tapiero, Charles S., 2008. "Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2565-2574.
    3. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.

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