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A dichotomy theorem for random walks on hypergroups

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Probability Measures on Groups IX

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1379))

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Abstract

We define possible and recurrent elements for random walks on commutative hypergroups and show that for a large class of random walks, either no elements is recurrent or all possible elements are recurrent and they form a closed subhypergroup.

née Ajit Kaur Chilana.

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References

  1. W. R. Bloom and H. Heyer, The Fourier transform for probability measures on hypergroups, Rend. di Mat. 2 (1982), 315–334.

    MathSciNet  MATH  Google Scholar 

  2. W. R. Bloom and H. Heyer, Convergence of convolution products of probability measures on hypergroups, Rend. di Mat 3 (1982), 547–563.

    MathSciNet  MATH  Google Scholar 

  3. K. L. Chung, A Course in Probability Theory (1968) Academic Press.

    Google Scholar 

  4. K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variable, Mem. Amer. Math. Soc. (1951), 1–12.

    Google Scholar 

  5. J. L. Doob, Stochastic Processes. John Wiley and Sons Inc. (1953) New York.

    MATH  Google Scholar 

  6. C. F. Dunkl, The measure algebra of a locally compact hypergroup, Trans Amer. Math. Soc. 179 (1973), 331–348.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Gallardo and O. Gebuhrer, Marches aleatoires et hypergroups, Expo. Math. 5(1987), 41–73.

    MathSciNet  MATH  Google Scholar 

  8. P. R. Halmos, Measure Theory, Van Nostrand 1950, Springer Verlag 1974 East West Press (New Delhi, Madras).

    Google Scholar 

  9. H. Heyer, Probability theory on hypergroups, Probability Measures on groups VII. Lecture notes in Math. 1064 (1984) 481–550.

    Article  MathSciNet  Google Scholar 

  10. R. I. Jewett, Spaces with an abstract convolution of measures, Adv. in Math. 18(1975), 1–101.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. L. Kelley, General Topology, (1955), Van Nostrand.

    Google Scholar 

  12. R. Lasser, Orthogonal Polynomials and hypergroups Rend. di Mat. (VII) 3,2 (1983), 185–209.

    MathSciNet  MATH  Google Scholar 

  13. R. M. Loynes, Products of Independent Random elements in a topological group, Z. Wahrscheinlichkeitstheorie verw. Geb. 1(1963), 446–455.

    Article  MathSciNet  MATH  Google Scholar 

  14. K. A. Ross, Centers of hypergroups, Trans. Amer. Math. Soc. 243 (1978), 251–269.

    Article  MathSciNet  MATH  Google Scholar 

  15. K. Schmidt. Cocycles on Ergodic Transformation groups, Macmillan 1976.

    Google Scholar 

  16. R. C. Vrem, Lecunarity on compact hypergroup, Math. Zeit. 164(1978) 93–104.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, 110 007, Delhi, India

    Ajay Kumar & Ajit Iqbal Singh

Authors
  1. Ajay Kumar
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  2. Ajit Iqbal Singh
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Editor information

Herbert Heyer

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© 1989 Springer-Verlag

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Kumar, A., Singh, A.I. (1989). A dichotomy theorem for random walks on hypergroups. In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087853

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  • DOI: https://doi.org/10.1007/BFb0087853

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51401-5

  • Online ISBN: 978-3-540-46206-4

  • eBook Packages: Springer Book Archive

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