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Abundo, Mario

The mean of the running maximum of an integrated Gauss-Markov process and the connection with its first-passage time. (English) Zbl 1364.60094

Stochastic Anal. Appl. 35, No. 3, 499-510 (2017).
Summary: 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.

Cited in 7 Documents

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G15 Gaussian processes
60G70 Extreme value theory; extremal stochastic processes
60J65 Brownian motion
60H05 Stochastic integrals
60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

Gauss-Markov process; running maximum; first-passage time; Brownian motion; Ornstein-Uhlenbeck process
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References:

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