Approximation Order Analysis for the Piecewise Linear Markov Method
Let S : [0, 1] --> [0, 1] be a mapping and let P : L-1 (0, 1) --> L-1 (0, 1) be the corresponding Frobenius-Perron operator. The method of Markov finite approximations has been proved theoretically and computationally a fast and efficient numerical approach to computing a fixed density of P. In this paper we give a strict analysis for the approximation order of the method applied to continuous functions.
Stochastic Analysis and Application
(2001). Approximation Order Analysis for the Piecewise Linear Markov Method. Stochastic Analysis and Application, 19(6), 911-923.
Available at: http://aquila.usm.edu/fac_pubs/3756