Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps

DOI10.1088/1361-6544/aa85d0zbMath1384.37042arXiv1702.00699OpenAlexW2586638697MaRDI QIDQ4597525

Juho Leppänen

Publication date: 13 December 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00699

zbMATH Keywords

rate of convergencecentral limit theoremfunctional correlation bound

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems involving maps of the interval (37E05)

Related Items (6)

Intermittent quasistatic dynamical systems: weak convergence of fluctuations ⋮ Sunklodas' approach to normal approximation for time-dependent dynamical systems ⋮ A note on the finite-dimensional distributions of dispersing billiard processes ⋮ Central limit theorems with a rate of convergence for time-dependent intermittent maps ⋮ Loss of memory and moment bounds for nonstationary intermittent dynamical systems ⋮ Functional correlation bounds and optimal iterated moment bounds for slowly-mixing nonuniformly hyperbolic maps

Cites Work

• Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equation
• Polynomial loss of memory for maps of the interval with a neutral fixed point
• Recurrence times and rates of mixing
• Central limit theorem and stable laws for intermittent maps
• Quasistatic dynamics with intermittency
• An almost sure ergodic theorem for quasistatic dynamical systems
• Invariance principles for interval maps with an indifferent fixed point
• Sharp polynomial estimates for the decay of correlations
• About the Berry-Esseen theorem for weakly dependent sequences
• Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard
• Berry--Esseen theorem and local limit theorem for non uniformly expanding maps
• Decay of correlation for random intermittent maps
• Statistical properties of a skew product with a curve of neutral points
• Some unbounded functions of intermittent maps for which the central limit theorem holds
• A probabilistic approach to intermittency
• Quasistatic dynamical systems
• Central limit theorems for sequential and random intermittent dynamical systems
• Decay of correlations for piecewise smooth maps with indifferent fixed points
• STABLE LIMITS FOR PROBABILITY PRESERVING MAPS WITH INDIFFERENT FIXED POINTS

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