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.
Abundo, M. (2018). Some remarks on the mean of the running maximum of integrated Gauss-Markov processes and their first-passage times. In Computer aided systems theory : EUROCAST 2017 (pp.72-79). Springer [10.1007/978-3-319-74727-9_9].
Some remarks on the mean of the running maximum of integrated Gauss-Markov processes and their first-passage times
Abundo, M
2018-01-01
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.File in questo prodotto:
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