Constructive approximations of Markov operators

Journal of Statistical Physics

Volumn 105, Issue 5-6, 2001, Pages 863-878

  Ding, Jiu ^a   Zhou, Aihui ^b  

^a University of Southern Mississippi   (United States)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Bounded variation; Fixed densities; Markov finite approximations; Markov operators

Indexed keywords

EID: 0035541853     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013553227865     Document Type: Article

References (17)

1. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems (Cambridge University Press, 1993).
2. C. Bose and R. Murray, The exact rate of approximation in Ulam's method, Disc. Cont. Dyna. Sys. 7(1):219-235 (2001).
3. P. G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, 1978).
4. J. Ding and T. Y. Li, Markov finite approximation of Frobenius Perron operator, Nonlinear Anal., TMA 17(8):759-772 (1991).
5. J. Ding and T. Y. Li, A convergence rate analysis for Markov finite approximations to a class of Frobenius-Perron operators, Nonlinear Anal., TMA 31(5/6):765-777 (1998).
6. J. Ding and A. Zhou, Piecewise linear Markov approximations of Frobenius Perron operators associated with multi-dimensional transformations, Nonlinear Anal., TMA 25(4):399-408 (1995).
7. S. Foguel, The Ergodic Theory of Markov Processes (Van Nostrand Mathematical Studies 21, 1969).
8. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, 1983).
9. E. Giusti, Minimal Surfaces and Functions of Bounded Variation (Birkhäuser, 1984).
10. N, Israel J. Math. 67(3):272-286 (1989).
11. G. Keller, Stochastic stability in some chaotic dynamical systems, Mon. Math. 94:313-353 (1982).
12. A. Lasota and M. Mackey, Chaos, Fractals, and Noises, 2nd edn. (Springer-Verlag, 1994).
13. A. Lasota and J. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186:481-488 (1973).
14. T. Y. Li, Finite approximation for the Frobenius-Perron operator, a solution to Ulam's conjecture, J. Approx. Theory 17:177-186 (1976).
15. R. Murray, Approximation error for invariant density calculations, Discrete and Cont. Dynam. Sys. 4(3):535-557 (1998).
16. M. J. Todd, The Computation of Fixed points and Applications (Springer-Verlag, 1976).
17. S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Math. 8 (Interscience, 1960).