On the distribution of ranked heights of excursions of a Brownian bridge.

DOI10.1214/aop/1008956334zbMath1033.60050OpenAlexW1594513799MaRDI QIDQ1872189

Marc Yor, Jim W. Pitman

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1008956334

zbMATH Keywords

exponential distributionBessel processlocal timePoisson point processbridgeexcursionhomogeneous functional

Mathematics Subject Classification ID

Brownian motion (60J65) Self-similar stochastic processes (60G18)

Related Items (9)

First Passage Time of Skew Brownian Motion ⋮ An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes ⋮ The distribution of the maximal difference between a Brownian bridge and its concave majorant ⋮ On excursions inside an excursion ⋮ Some explicit Krein representations of certain subordinators, including the gamma process ⋮ Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score ⋮ On exact simulation algorithms for some distributions related to Jacobi theta functions ⋮ Gaps and interleaving of point processes in sampling from a residual allocation model ⋮ The asymptotic distribution of the diameter of a random mapping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An introduction to the theory of point processes
• Excursions in Brownian motion
• Laplace transforms related to excursions of a one-dimensional diffusion
• The law of the maximum of a Bessel bridge
• Random Brownian scaling identities and splicing of Bessel processes
• On the distribution of Brownian areas
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• The distribution of time spent by a standard excursion above a given level, with applications to ring polymers near a discontinuity in potential
• Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
• A Contribution to Renewal Theory
• Fluctuation identities for lévy processes and splitting at the maximum
• Arcsine Laws and Interval Partitions Derived from a Stable Subordinator
• Ranked functionals of Brownian excursions
• Brownian bridge asymptotics for random mappings
• CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE
• Semi-Stable Stochastic Processes
• A Stochastic Approach to the Gamma Function
• Semi-stable Markov processes. I
• Zero-Free Intervals of Semi-Stable Markov Processes.
• K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests
• Branching Processes Since 1873
• Brownian Local Times and Taboo Processes
• Heuristic Approach to the Kolmogorov-Smirnov Theorems
• The Influence of the Maximum Term in the Addition of Independent Random Variables
• Asymptotic properties of ranked heights in Brownian excursions

This page was built for publication: On the distribution of ranked heights of excursions of a Brownian bridge.