Markov switching for position dependent random maps with application to forecasting

SIAM Journal on Applied Dynamical Systems

Volumn 4, Issue 2, 2005, Pages 391-406

  Bahsount, Wael ^a   Gora, Paweł ^b   Boyarsky, Abraham ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Absolutely continuous invariant measure; Frobenius Perron operator; Markov switching; Random map

Indexed keywords

MAPS; MARKOV PROCESSES; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA;

ABSOLUTELY CONTINUOUS INVARIANT MEASURE; FROBENIUS-PERRON OPERATORS; MARKOV SWITCHING; RANDOM MAP;

FORECASTING;

EID: 25144439303     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040604042     Document Type: Article

References (14)

1. W. BAHSOUN, P. GÓRA, AND A. BOYARSKY, Stochastic perturbations for position dependent random maps, Stoch. Dyn., 3 (2003), pp. 545-557.
2. W. BAHSOUN AND P. GÓRA, Weakly convex and concave random maps with position dependent probabilities, Stochastic Anal. Appl., 21 (2003), pp. 983-994.
3. C. BOSE, V. MAUME-DESCHAMPS, B. SCHMITT, AND S. SHIN, Invariant measures for piecewise convex transformations of an interval, Studia Math., 152 (2002), pp. 263-297.
4. V. BALADI, Positive Transfer Operators and Decay of Correlations, Adv. Ser. Nonlinear Dynam. 16, World Scientific Publishing, River Edge, NJ, 2000.
5. A. BOYARSKY AND P. GÓRA, Laws of Chaos, Birkhaüser Boston, Boston, 1997.
6. J. DOOB, Stochastic Processes, Wiley, New York, 1953.
7. N. DUNFORD AND J. T. SCHWARTZ, Linear Operators, Part I: General Theory, Interscience, New York, 1964.
8. G. FROYLAND, Ulam's method for random interval maps, Nonlinearity, 12 (1999), pp. 1029-1052.
9. N, Israel J. Math., 67 (1989), pp. 272-286.
10. J. D. HAMILTON, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), pp. 357-384.
11. S. PELIKAN, Invariant densities for random maps of the interval, Trans. Amer. Math. Soc., 281 (1984), pp. 813-825.
12. S. R. PLISKA, Introduction to Mathematical Finance: Discrete Time Models, Blackwell Publishers, Oxford, UK, 1997.
13. D. RUELLE, Spectral properties of a class of operators associated with maps in one dimension, Ergodic Theory Dynam. Systems, 11 (1991), pp. 757-767.
14. K. R. SCHENK-HOPPË, Random dynamical systems in economics, Stoch. Dyn., 1 (2001), pp. 63-83.