Error estimates of the Markov finite approximation of the Frobenius-Perron operator

Abstract

IN THE practical application of the modern ergodic theory, one of the main problems is related to the computation of the absolutely continuous invariant measures for nonsingular transformations on measure spaces (see Lasota and Mackey [l]). A simple example is constructed in Li [2] to show that the round-off error can completely dominate the calculation if one is to compute the invariant measure directly using a sequence of Cesaro sums. An alternative is to compute the invariant density function for the Frobenius-Perron operator P,: L’(0, 1) + L’(0, 1) associated with the nonsingular measurable transformations S: [0, 11 + [0, 11. The Frobenius-Perron operator P, is defined by