An Asymptotic Result for Non Crossing Probabilities of Brownian Motion with Trend

DOI10.1080/03610920701386943zbMath1137.60023OpenAlexW2043985427MaRDI QIDQ5438336

Wolfgang Bischoff, Juerg Hüsler, Enkelejd Hashorva

Publication date: 23 January 2008

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610920701386943

zbMATH Keywords

large deviationsasymptotic resultsboundary crossing probabilityBrownian motion with trendBrownian bridge with trend

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Gaussian processes (60G15) Linear regression; mixed models (62J05) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Large deviations (60F10) Markov processes: hypothesis testing (62M02)

Related Items (4)

Boundary noncrossings of additive Wiener fields ⋮ Boundary non-crossing probabilities for Slepian process ⋮ Boundary non-crossing probabilities of Gaussian processes: sharp bounds and asymptotics ⋮ Boundary non-crossing probabilities for fractional Brownian motion with trend

Cites Work

• Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests
• Asymptotics of a boundary crossing probability of a Brownian bridge with general trend
• On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models.
• Asymptotics and bounds for multivariate Gaussian tails
• Some conditional crossing results of Brownian motion over a piecewise-linear boundary
• Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test
• A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend
• Boundary crossing probability for Brownian motion
• Brownian Type Boundary Crossing Probabilities for Piecewise Linear Boundary Functions
• Boundary crossing probability for Brownian motion and general boundaries
• Approximations of boundary crossing probabilities for a Brownian motion
• On Certain Confidence Contours for Distribution Functions

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