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Limit theorems for random walks with dynamical random transitions
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  • Published: September 1994

Limit theorems for random walks with dynamical random transitions

  • Michael Lin1,
  • Ben-Zion Rubshtein1 &
  • Rainer Wittmann2 

Probability Theory and Related Fields volume 100, pages 285–300 (1994)Cite this article

  • 72 Accesses

  • 4 Citations

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Summary

Let θ be an ergodic and conservative non-singular transformation of (Ω, Σ,m) (thedynamic environment), let μ w be a random probability on a locally compact second countable groupG, and define

$$v_{_w }^{(n)} = \mu _{\theta ^n } - 1_w *\mu _{\theta ^n } - 2_w *...*\mu _{\theta w} *\mu _w $$

Conditions for the convergence lim n→∞∥v (n)ω *(f−δt*f)∥1=0 for a.e. ω and everyf∈L 1(G) andt∈G, are given, whenG is Abelian or compact.

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Author information

Authors and Affiliations

  1. Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Michael Lin & Ben-Zion Rubshtein

  2. Institut für Mathematische Stochastik, Lotzetrasse 13, D-37083, Göttingen, Germany

    Rainer Wittmann (Heisenberg fellow of the Deutsche Forschungsgemeinschaft)

Authors
  1. Michael Lin
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  2. Ben-Zion Rubshtein
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  3. Rainer Wittmann
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Additional information

Research partially supported by the Israel Ministry of Science

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Lin, M., Rubshtein, BZ. & Wittmann, R. Limit theorems for random walks with dynamical random transitions. Probab. Th. Rel. Fields 100, 285–300 (1994). https://doi.org/10.1007/BF01193702

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  • Received: 26 October 1993

  • Revised: 25 April 1994

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01193702

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Mathematics Subject Classification (1991)

  • 60J15
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