High order approximation of the Frobenius-Perron operator

摘要

We formulate a general convergence theory for the finite dimensional projection approximation of the fixed point of a class of linear operators. In particular, we explore the relation with the standard framework of stability and consistency of the approximation imply convergence. Applications include the Frobenius-Perron operator PS, corresponding to a nonsingular measurable transformation from [0, 1] to itself. Numerical experiments are also given to support the theoretical analysis.