Uniqueness of Invariant Densities for Certain Random Maps of The Interval
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 301-308

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A random map is a discrete time process in which one of a number of maps, M, is chosen at random at each stage and applied. In this note we study a random map, where M is a set of piecewise linear Markov maps on [0, 1]. Sufficient conditions are presented which allow the determination of the unique absolutely continuous invariant measure of the process.
DOI : 10.4153/CMB-1987-043-1
Mots-clés : 28D99, 60G99
Boyarsky, Abraham. Uniqueness of Invariant Densities for Certain Random Maps of The Interval. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 301-308. doi: 10.4153/CMB-1987-043-1
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[1] 1. Lasota, A. and Yorke, J.A., On the Existence of Invariant Measures for Piecewise Monotonie Transformations, Trans. Amer. Math Soc. 186 (1973), pp. 481–488. Google Scholar

[2] 2. Boyarsky, A. and Scarowsky, M., On a Class of Transformations which have Unique Absolutely Continuous Invariant Measures, Trans. Amer. Math. Soc, 255 (1979), pp. 243–262. Google Scholar

[3] 3. Friedman, N. and Boyarsky, A., Matrices and Eigenfunctions Induced by Markov Maps, Linear Algebra Appl. 38(1981), pp. 141–147. Google Scholar

[4] 4. Friedman, N. and Boyarsky, A., Irreducibility and Primitivity Using Markov Maps, Linear Algebra Appl. 37 (1981) pp. 103–117. Google Scholar

[5] 5. Dunford, N. and Schwartz, J.T., Linear Operators, Part I, J. Wiley, New York, 1967. Google Scholar

[6] 6. Pelikan, S., Invariant Densities for Random Maps of the Interval, Trans. Amer. Math. Soc. 281, No. 2, (1984), pp. 813–825. Google Scholar

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