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Random Iteration of I.I.D. Quadratic Maps

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Stochastics in Finite and Infinite Dimensions

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Abstract

Let,and be an i,i.d. sequence with values in [0, 4]. Let be a Markov chain defined by the random iteration scheme.In this paper we present a survey of recent results on the existence and uniqueness of nontrivial invariant probability measures for. A brief review of the deterministic case is also included.

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Athreya, K.B., Bhattacharya, R.N. (2001). Random Iteration of I.I.D. Quadratic Maps. In: Hida, T., Karandikar, R.L., Kunita, H., Rajput, B.S., Watanabe, S., Xiong, J. (eds) Stochastics in Finite and Infinite Dimensions. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0167-0_3

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  • DOI: https://doi.org/10.1007/978-1-4612-0167-0_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6643-3

  • Online ISBN: 978-1-4612-0167-0

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