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Recurrent random walks in nonnegative matrices II
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  • Published: December 1993

Recurrent random walks in nonnegative matrices II

  • Arunava Mukhrjea1 

Probability Theory and Related Fields volume 96, pages 415–434 (1993)Cite this article

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Summary

In this paper, we continue the study undertaken in our earlier paper [M1]. One of the main results here can be described as follows. LetX 0,X 1, ... be a sequence of iid random affine maps from (R +)d into itself. Let us write:W n ≡X n X n −1...X 0 andZ n ≡X 0 X 1...X n , where “composition” of maps is the rule of multiplication. By the attractorA(u),u∈(R +)d, we mean the setA u={y∈(R+)d:P(Wn u∈N i.o.) > 0 for every openN containingy}. It is shown that the attractorA(u), under mild conditions, is the support of a stationary probability measure, when the random walk (Z n ) has at least one recurrent state.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of South Florida, 33620-5700, Tampa, FL, USA

    Arunava Mukhrjea

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  1. Arunava Mukhrjea
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Mukhrjea, A. Recurrent random walks in nonnegative matrices II. Probab. Th. Rel. Fields 96, 415–434 (1993). https://doi.org/10.1007/BF01200204

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  • Received: 10 September 1992

  • Revised: 11 February 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01200204

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Mathematics Subject Classifications (1991)

  • 60 B 10
  • 60 J 15
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