Borel–Cantelli lemmas and extreme value theory for geometric Lorenz models

DOI10.1088/0951-7715/29/1/232zbMath1361.37013arXiv1404.1656OpenAlexW2963354979WikidataQ125057530 ScholiaQ125057530MaRDI QIDQ3466422

Licheng Zhang

Publication date: 1 February 2016

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1656

zbMATH Keywords

Lorenz systemBorel-Cantelli lemmasextreme value lawsrare events points process

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Strong limit theorems (60F15) Dynamical systems and their relations with probability theory and stochastic processes (37A50)

Related Items (4)

Almost sure convergence of maxima for chaotic dynamical systems ⋮ Simultaneous action of finitely many interval maps: some dynamical and statistical properties ⋮ Hitting times distribution and extreme value laws for semi-flows ⋮ Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems

Uses Software

• RODES

Cites Work

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• Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
• On the link between dependence and independence in extreme value theory for dynamical systems
• Hitting time statistics and extreme value theory
• Extremes and related properties of random sequences and processes
• Structural stability of Lorenz attractors
• A rigorous ODE solver and Smale's 14th problem
• Central limit theorems for the shrinking target problem
• Statistics of closest return for some non-uniformly hyperbolic systems
• Convergence of rare event point processes to the Poisson process for planar billiards
• Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence
• Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps
• Extreme value theory for non-uniformly expanding dynamical systems
• A Metrical Theorem in Diophantine Approximation
• The Lorenz attractor exists
• Deterministic Nonperiodic Flow
• Metrical Theorems on Fractional Parts of Sequences

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