Extreme value theory for dependent sequences via the Stein-Chen method of Poisson approximation

DOI10.1016/0304-4149(88)90092-0zbMath0661.60033OpenAlexW1998949846MaRDI QIDQ1113170

Richard L. Smith

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0304-4149(88)90092-0

zbMATH Keywords

error estimatesextreme value theorylocal dependenceCompound Poisson limit resultsextreme values in a random sequence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (7)

Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and -statistics ⋮ Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences ⋮ Continued fractions, the Chen–Stein method and extreme value theory ⋮ Extreme values for characteristic radii of a Poisson-Voronoi tessellation ⋮ Inequalities for rare events in time-reversible Markov chains. II ⋮ A general study of extremes of stationary tessellations with examples ⋮ Poisson approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Extremes and related properties of random sequences and processes
• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Extreme value theory for suprema of random variables with regularly varying tail probabilities
• On the exceedance point process for a stationary sequence
• Asymptotic expansions in the Poisson limit theorem
• Poisson approximation for dependent trials
• On the rate of Poisson convergence
• Asymptotic approximation of crossing probabilities of random sequences
• Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli Trials
• Extreme values of non-stationary random sequences
• The rate of convergence of extremes of stationary normal sequences
• Poisson approximation for some statistics based on exchangeable trials

This page was built for publication: Extreme value theory for dependent sequences via the Stein-Chen method of Poisson approximation