The mean of the running maximum of an integrated Gauss–Markov process and the connection with its first-passage time

DOI10.1080/07362994.2016.1273784zbMath1364.60094OpenAlexW2578303252MaRDI QIDQ2986700

Mario Abundo

Publication date: 16 May 2017

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2016.1273784

zbMATH Keywords

Brownian motionOrnstein-Uhlenbeck processrunning maximumfirst-passage timeGauss-Markov process

Mathematics Subject Classification ID

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

Related Items (7)

On short-term loan interest rate models: a first passage time approach ⋮ One-sided maximal inequalities for a randomly stopped Bessel process ⋮ A first-passage-place problem for integrated diffusion processes ⋮ The arctangent law for a certain random time related to one-dimensional diffusions ⋮ Fractional Ornstein-Uhlenbeck process with stochastic forcing, and its applications ⋮ A fractional PDE for first passage time of time-changed Brownian motion and its numerical solution ⋮ Fractionally integrated Gauss-Markov processes and applications

Cites Work

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• On an approach to boundary crossing by stochastic processes
• An inverse first-passage problem for one-dimensional diffusions with random starting point
• On the maximum of the generalized Brownian bridge
• Some conditional crossing results of Brownian motion over a piecewise-linear boundary
• Limit at Zero of the First-Passage Time Density and the Inverse Problem for One-Dimensional Diffusions
• FROM BOUNDARY CROSSING OF NON-RANDOM FUNCTIONS TO BOUNDARY CROSSING OF STOCHASTIC PROCESSES

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