We find explicit formulae for the mean of the running maximum of conditional and unconditional Brownian motion; they are used to obtain the mean, a(t), of the running maximum of an integrated Gauss–Markov process. Then, we deal with the connection between the moments of its first-passage-time and a(t). As explicit examples, we consider integrated Brownian motion and integrated Ornstein–Uhlenbeck process.
Abundo, M. (2017). The mean of the running maximum of an integrated Gauss-Markov process and the connection with its first-passage time. STOCHASTIC ANALYSIS AND APPLICATIONS, 35(3), 499-510 [10.1080/07362994.2016.1273784].
The mean of the running maximum of an integrated Gauss-Markov process and the connection with its first-passage time.
Abundo Mario
2017-01-01
Abstract
We find explicit formulae for the mean of the running maximum of conditional and unconditional Brownian motion; they are used to obtain the mean, a(t), of the running maximum of an integrated Gauss–Markov process. Then, we deal with the connection between the moments of its first-passage-time and a(t). As explicit examples, we consider integrated Brownian motion and integrated Ornstein–Uhlenbeck process.| File | Dimensione | Formato | |
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