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International Conference on Distributed Computer and Communication Networks

DCCN 2017: Distributed Computer and Communication Networks pp 135–145Cite as

Bounding the Risk Probability

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 700))

Abstract

For some safety–critical applications, it is important to calculate the probability that a discrete time autoregressive (AR) process leaves a given interval at least once during a certain period of time. For example, such AR process can be interpreted as a temporally correlated safety indicator and the interval as a target zone of the process. It is assumed that the safety of the system under surveillance is compromised if the above-mentioned probability becomes too important. This problem has been previously studied in the case of known distributions of the innovation process. Let us assume now that the distributions of the innovation and initial state are unknown but some special bounds for the cumulative distribution functions and/or for the probability density functions are available. Numerical methods to calculate the bounds for the above-mentioned probability are considered in the paper.

I. Nikiforov—The author gratefully acknowledges the research and financial support of this work from the Thales Alenia Space, France.

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Acknowledgments

The author gratefully acknowledges the research and financial support of this work from the Thales Alenia Space, France.

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Authors and Affiliations

  1. Université de Technologie de Troyes, UTT/ICD/LM2S, UMR 6281, CNRS, 12, rue Marie Curie, CS 42060, 10004, Troyes Cedex, France

    Igor Nikiforov

Authors
  1. Igor Nikiforov
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Correspondence to Igor Nikiforov .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Nikiforov, I. (2017). Bounding the Risk Probability. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol 700. Springer, Cham. https://doi.org/10.1007/978-3-319-66836-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-66836-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66835-2

  • Online ISBN: 978-3-319-66836-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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