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

  • Marco Abundo
  • Mario AbundoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10672)

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.

Keywords

Running maximum First-passage time Gauss-Markov process 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Tor Vergata UniversityRomeItaly

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