Computing Invariant Densities of a Class of Piecewise Increasing Mappings

Author:

Wang Zi1ORCID,Ding Jiu2,Rhee Noah3

Affiliation:

1. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China

2. School of Mathematics and Natural Sciences, The University of Southern Mississippi, Hattiesburg, MS 39406, USA

3. Department of Mathematics and Statistics, University of Missouri – Kansas City, Kansas City, MO 64110, USA

Abstract

Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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