Login | Register

SRB measures for certain Markov processes


SRB measures for certain Markov processes

GÓRA, PAWEŁ and Bahsoun, Wael (2011) SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems, 30 (1). pp. 17-37. ISSN 1078-0947

Text (application/pdf)
gora2011.pdf - Accepted Version

Official URL: http://dx.doi.org/10.3934/dcds.2011.30.17


We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then, when all the constituent maps have common fixed points at 0 and 1, theorems are given to analyze properties of the ergodic invariant measures and . In particular, sufficient conditions for and/or to be, or not to be, SRB measures are given. We apply some of our results to asset market games.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Authors:GÓRA, PAWEŁ and Bahsoun, Wael
Journal or Publication:Discrete and Continuous Dynamical Systems
Digital Object Identifier (DOI):10.3934/dcds.2011.30.17
Keywords:Iterated Function System, SRB-Measures.
ID Code:976826
Deposited On:29 Jan 2013 14:05
Last Modified:18 Jan 2018 17:43


1 L. Arnold, "Random Dynamical Systems," Springer Verlag, Berlin, 1998.

2 A. Boyarsky and P. Góra, "Laws of Chaos," Brikhäuser, Boston, 1997.

3 J. Buzzi, Absolutely continuous S.R.B. measures for random Lasota-Yorke maps, Trans. Amer. Math. Soc., 352 (2000), 3289-3303.

4 I. Evstigneev, T. Hens and K. R. Schenk-Hoppé, Market selection of financial trading strategies: Global stability, Math. Finance, 12 (2002), 329-339.

5 P. Diaconis and D. Freedman, Iterated random functions, SIAM Rev., 41 (1999), 45-76.

6 R. Drogin, An invariance principle for martingales, Ann. Math. Statist., 43 (1972), 602-620.

7 L. Dubins and D. Freedman, Invariant probabilities for certain Markov processes, Ann. Math. Statist., 37 (1966), 837-848.

8 P. Hall and C. Heyde, "Martingale Limit Theory and Its Application," Academic Press, New York-London, 1980.

9 J. L. Kelly, A new interpretation of information rate, Bell Sys. Tech. J., 35 (1956), 917-926.

10 Y. Kifer, "Ergodic Theory of Random Transformations," Birkhäuser, Boston, 1986.

11 P.-D. Liu, Dynamics of random transformations: smooth ergodic theory, Ergodic Theory Dynam. Syst., 21 (2001), 1279-1319.

12 A. N. Shiryaev, "Probability," Springer-Verlag, New York, 1984.

13 Ö. Stenflo, Uniqueness of invariant measures for place-dependent random iterations of functions, in "Fractals in Multimedia" (eds. M. F. Barnsley, D. Saupe and E. R. Vrscay), Springer, (2002), 13-32.

14 L.-S. Young, What are SRB measures, and which dynamical systems have them?, J. Statist. Phys., 108 (2002), 733-754.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top