Birkhoff's Ergodic Theorem and the Piecewise-Constant Maximum Entropy Method for Frobenius-Perron Operators
Mathematics and Natural Sciences
Let (X, Σ, σ) be a finite measure space and S: X→X be a nonsingular transformation such that the corresponding Frobenius–Perron operator P S : L 1(X)→L 1(X) has a stationary density f*. We propose a piecewise-constant maximum entropy method for the numerical recovery of f* and give its relation to the classic Birkhoff's individual ergodic theorem. An advantage of the piecewise-constant method over the current maximum entropy method based on polynomial basis functions is that a nonlinear system of equations is not needed for solving the related moment problem. Numerical results are given for several one dimensional test mappings.
International Journal of Computer Mathematics
(2012). Birkhoff's Ergodic Theorem and the Piecewise-Constant Maximum Entropy Method for Frobenius-Perron Operators. International Journal of Computer Mathematics, 89(8), 1083-1091.
Available at: https://aquila.usm.edu/fac_pubs/20968