Asymptotic behavior of conditional laws and moments of \(\alpha\)-stable random vectors, with application to upcrossing intensities

DOI10.1214/aop/1022677455zbMath0963.60006OpenAlexW1550247684MaRDI QIDQ1568294

J. M. P. Albin, M. Ross Leadbetter

Publication date: 21 June 2001

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

Full work available at URL: https://doi.org/10.1214/aop/1022677455

zbMATH Keywords

momentconditional probabilityconditional moment\(\alpha\)-stable distributioncrossingupcrossingskewed \(\alpha\)-stable distributionupcrossing intensity

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Asymptotic distribution theory in statistics (62E20) Limit theorems in probability theory (60F99)

Related Items (3)

Extremes and upcrossing intensities for \(P\)-differentiable stationary processes. ⋮ On extremes and streams of upcrossing. ⋮ An interview with Ross Leadbetter

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distributions of subadditive functionals of sample paths of infinitely divisible processes
• The expected number of level crossings for stationary, harmonisable, symmetric, stable processes
• Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes
• Extremes and related properties of random sequences and processes
• Extrema of skewed stable processes
• Conditional moments and linear regression for stable random variables
• Level crossings of a stochastic process with absolutely continuous sample paths
• How do conditional moments of stable vectors depend on the spectral measure?
• Level crossings of absolutely continuous stationary symmetric \(\alpha\)-stable processes
• Extremes for non-anticipating moving averages of totally skewed \(\alpha\)-stable motion
• Domains of attraction of stable measures on a Hilbert space
• The expected number of level crossings for certain symmetric α-stable processes
• On Crossings of Levels and Curves by a Wide Class of Stochastic Processes
• A Useful Convergence Theorem for Probability Distributions
• Mathematical Analysis of Random Noise
• Mathematical Analysis of Random Noise

This page was built for publication: Asymptotic behavior of conditional laws and moments of \(\alpha\)-stable random vectors, with application to upcrossing intensities