Some Remarks on the Mean of the Running Maximum of Integrated Gauss-Markov Processes and Their First-Passage Times
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.
KeywordsRunning maximum First-passage time Gauss-Markov process
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