Darling-Erdős theorems for normalized sums of i. i. d. variables close to a stable law
From MaRDI portal
Publication:1307507
DOI10.1214/aop/1022855652zbMath0943.60041OpenAlexW1527493561MaRDI QIDQ1307507
Publication date: 4 September 2000
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1022855652
convergence in distributionGumbel distributionstrictly stable lawspectrally negative Ornstein-Uhlenbeck processes
Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Sums of independent random variables; random walks (60G50)
Related Items
A general Darling-Erdős theorem in Euclidean space, Darling-Erdős theorem for self-normalized sums, On the asymptotic of the maximal weighted increment of a random walk with regularly varying jumps: the boundary case, Darling--Erd\H{o}s theorem for L\'evy processes at zero, Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A limit theorem for the maximum of normalized sums of independent random variables
- On extremal theory for stationary processes
- Extreme value theory for moving average processes
- Extension of the Darling and Erdős theorem on the maximum of normalized sums
- The growth of random walks and Levy processes
- Extremes of moving averages of stable processes
- The Darling-Erdős theorem for sums of i.i.d. random variables
- One-sided local large deviation and renewal theorems in the case of infinite mean
- Darling-Erdős theorems for martingales
- Maxima and exceedances of stationary Markov chains
- Fluctuation theory in continuous time
- Refined Large Deviation Limit Theorems
- A Delicate Law of the Iterated Logarithm for Non-Decreasing Stable Processes
- A Limit Theoerm for Random Variables with Infinite Moments
- Large deviations of sums of independent random variables
