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Random Iterations of Two Quadratic Maps

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Abstract

We study invariant measures of Markov processes obtained by the action of successive independent iterations of a map chosen at random from a set of two quadratic maps.

Research was supported in part by NSF Grant DMS 9206937

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References

  1. Barnsley, M.F. and Elton, J.H. (1988). A new class of Markov processes for image encoding. Adv. Appl. Prob. 20 14–32.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bhattacharya, R.N. and Lee, O. (1988). Asymptotics of a class of Markov processes which are not in general irreducible. Ann. Probab. 16 1333–1347,

    Article  MathSciNet  MATH  Google Scholar 

  3. Correction, ibid Bhattacharya, R.N. and Lee, O. Asymptotics of a class of Markov processes which are not in general irreducible. Ann. Probab. 16 1333–1347, (lap) (1992).

    Article  MathSciNet  Google Scholar 

  4. Collet, P. and Eckman, J-P. (1980). Iterated Maps on the Interval as Dynamical Systems. Birkhauser, Boston.

    MATH  Google Scholar 

  5. Devaney, R.L. (1989). An Introduction to Chaotic Dynamical Systems, Second Ed., Addison-Wesley, New York.

    MATH  Google Scholar 

  6. Dubins, L. E. and Freedman, D.A. (1966). Invariant probabilities for certain Markov processes. Ann. Math. Statist. 37 837–847.

    Article  MathSciNet  MATH  Google Scholar 

  7. Katok, A. and Kifer, Y. (1986). Random perturbations of transformations of an interval. J. D’Analyse Math. 47 193–237.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kifer, Y. (1986). Ergodic Theory of Random Transformations. Birkhauser, Boston.

    MATH  Google Scholar 

  9. Kifer, Y. (1988). Random Perturbations of Dynamical Systems. Birkhauser, Boston.

    MATH  Google Scholar 

  10. Ruelle, D. (1989). Chaotic Evolution and Strange Attractors. Cambridge Univ. press, Cambridge.

    Book  MATH  Google Scholar 

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© 1993 Springer-Verlag New York, Inc.

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Bhattacharya, R.N., Rao, B.V. (1993). Random Iterations of Two Quadratic Maps. In: Cambanis, S., Ghosh, J.K., Karandikar, R.L., Sen, P.K. (eds) Stochastic Processes. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7909-0_3

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  • DOI: https://doi.org/10.1007/978-1-4615-7909-0_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4615-7911-3

  • Online ISBN: 978-1-4615-7909-0

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