Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean
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Publication:2274274
DOI10.1016/j.spa.2018.11.015zbMath1422.60050arXiv1706.07369OpenAlexW2714650873MaRDI QIDQ2274274
Marc Kesseböhmer, Tanja I. Schindler
Publication date: 19 September 2019
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.07369
strong law of large numbersspectral methodtransfer operatoralmost sure convergence theoremspiecewise expanding interval maptrimmed sum process
Stationary stochastic processes (60G10) Dynamical aspects of measure-preserving transformations (37A05) Strong limit theorems (60F15) Ergodic theorems, spectral theory, Markov operators (37A30)
Related Items (6)
Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems ⋮ Prime numbers in typical continued fraction expansions ⋮ A note on large deviations for unbounded observables ⋮ Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails ⋮ Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type
Cites Work
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- On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps
- Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps
- On the rate of convergence of the St. Petersburg game
- A Bernstein type inequality and moderate deviations for weakly dependent sequences
- A nonstandard law of the iterated logarithm for trimmed sums
- On the mixing coefficients of piecewise monotonic maps
- Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties
- Basic properties of strong mixing conditions. A survey and some open questions
- Almost sure invariance principle for dynamical systems by spectral methods
- A vector-valued almost sure invariance principle for hyperbolic dynamical systems
- A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
- Estimates for partial sums of continued fraction partial quotients
- Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov. (Limit theorems for a class of Markov chains and applications to Anosov diffeomorphisms)
- Ergodic properties of invariant measures for piecewise monotonic transformations
- Ratios of trimmed sums and order statistics
- On the ergodic theory of non-integrable functions and infinite measure spaces
- Mixing: Properties and examples
- On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi-Perron algorithm
- Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean
- Some metric properties of \(\alpha\)-continued fractions.
- Limit theorems for nonnegative independent random variables with truncation
- Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
- Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
- Limit theory for some positive stationary processes with infinite mean
- Continuous phase transitions for dynamical systems
- Berry--Esseen theorem and local limit theorem for non uniformly expanding maps
- Trimmed sums for non-negative, mixing stationary processes.
- Infinite Ergodic Theory of Numbers
- A More General Maximal Bernstein-type Inequality
- Bernstein inequality and moderate deviations under strong mixing conditions
- Laws of the iterated logarithm for sums of the middle portion of the sample
- The Nagaev-Guivarc’h method via the Keller-Liverani theorem
- Limit theorems in dynamical systems using the spectral method
- Relative stability of trimmed sums
- WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS
- Bounded variation and invariant measures
- On the Existence of Invariant Measures for Piecewise Monotonic Transformations
- The strong law of large numbers when extreme terms are excluded from sums
- Stability for sums of i.i.d. random variables when extreme terms are excluded
- Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points
- Convergence in distribution of lightly trimmed and untrimmed sums are equivalent
- LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
- Pointwise convergence of Birkhoff averages for global observables
- The Effect of Trimming on the Strong Law of Large Numbers
- Dynamical Borel–Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems
- Quantitative ergodic theorems for weakly integrable functions
- Probability theory. A comprehensive course
- Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
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