A Quadratic Spline Projection Method For Computing Stationary Densities of Random Maps

Authors

Azzah Alshekhi, Al-Baha University
Jiu Ding, University of Southern MississippiFollow
Noah Rhee, University of MissouriFollow

Document Type

Article

Publication Date

2-1-2024

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We propose a quadratic spline projection method that computes stationary densities of random maps with position-dependent probabilities. Using a key variation inequality for the corresponding Markov operator, we prove the norm convergence of the numerical scheme for a family of random maps consisting of the Lasota–Yorke class of interval maps. The numerical experimental results show that the new method improves the L¹ -norm errors and increases the convergence rate greatly, compared with the previous operator-approximation-based numerical methods for random maps.

Publication Title

Communications in Mathematical Sciences

Volume

22

Issue

2

First Page

519

Last Page

531

Recommended Citation

Alshekhi, A., Ding, J., Rhee, N. (2024). A Quadratic Spline Projection Method For Computing Stationary Densities of Random Maps. Communications in Mathematical Sciences, 22(2), 519-531.
Available at: https://aquila.usm.edu/fac_pubs/21662