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Some Remarks on the Mean of the Running Maximum of Integrated Gauss-Markov Processes and Their First-Passage Times

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Computer Aided Systems Theory – EUROCAST 2017 (EUROCAST 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10672))

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Abstract

Explicit formulae for the mean of the running maximum of conditional and unconditional Brownian motion are found; these formulae are used to obtain the mean, a(t), of the running maximum of an integrated Gauss-Markov process X(t). Moreover, the connection between the moments of the first-passage-time of X(t) and a(t) is investigated. Some explicit examples are reported.

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References

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Author information

Authors and Affiliations

  1. Tor Vergata University, Rome, Italy

    Marco Abundo & Mario Abundo

Authors
  1. Marco Abundo
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  2. Mario Abundo
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Correspondence to Mario Abundo .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Abundo, M., Abundo, M. (2018). Some Remarks on the Mean of the Running Maximum of Integrated Gauss-Markov Processes and Their First-Passage Times. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-74727-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74726-2

  • Online ISBN: 978-3-319-74727-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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