A posteriori error estimates for Markov approximations of Frobenius-Perron operators

DOI10.1016/J.NA.2006.06.028zbMath1119.41018OpenAlexW2039870803MaRDI QIDQ881609

Aihui Zhou, Congming Jin, Jiu Ding

Publication date: 30 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.06.028

zbMATH Keywords

error estimatesFrobenius-Perron operatorinvariant measureMarkov approximation

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical solutions to equations with linear operators (65J10) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (1)

Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis

Cites Work

• Absolutely continuous invariant measures for piecewise expanding \(C^ 2\) transformations in \(\mathbb R^N\)
• Stochastic stability in some chaotic dynamical systems
• Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Approximation error for invariant density calculations
• Finite approximations of Frobenius-Perron operators. A solution of Ulam's conjecture to multi-dimensional transformations
• Rigorous numerical investigation of the statistical properties of piecewise expanding maps. A feasibility study
• Structure preserving finite element approximations of Markov operators
• Markov finite approximation of Frobenius-Perron operator
• Error estimates of the Markov finite approximation of the Frobenius-Perron operator
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• On the Approximation of Complicated Dynamical Behavior
• Approximating physical invariant measures of mixing dynamical systems in higher dimensions
• A convergence rate analysis for markov finite approximations to a class of Frobenius-Perron operators
• On estimating absolutely continuous invariant measures
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