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Ergodic Theory and Related Topics III pp 114–123Cite as

On the construction of generalized measure preserving transformations with given marginals

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1514))

Abstract

Measure preserving transformations generate stationary processes and vice versa. Which processes (X i ) correspond to the class of generalized measure preserving trans-formations? We give necessary conditions and show that they are sufficient for 2-valued processes as far as the marginals of (X 0, X 1, X 2, X 3) are concerned. The general problem remains open. Our main tool is a construction of a class of generalized measure preserving transformations which may be of independent interest.

Research partially supported by NSF Grant DMS-89-01267 and a Fulbright Research Grant.

This research was done during a visit of the second author at the Georgia Institute of Technology, Atlanta. This visit was supported by the Deutsche Forschungsgemeinschaft.

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References

  1. Krengel, U. Generalized measure preserving transformations, Proceed. Conf. on Almost Everywhere Convergence, Ohio Stat Univ. 1988, Academic Press (1989), 215–235.

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  2. Lin, M. and R. Wittmann. Pointwise ergodic theorems for certain order preserving mappings in L 1, to appear in Proceed. Conf. on Almost Everywhere Convergence II, Evanston, 1989.

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Author information

Authors and Affiliations

  1. Georgia Institute of Technology, School of Mathematics, 30332, Atlanta, GA, USA

    Theodore P. Hill

  2. Institut für Mathematische Stochastik, Univ. Göttingen, Lotzestr. 13, W-3400, Göttingen, Germany

    Ulrich Krengel

Authors
  1. Theodore P. Hill
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  2. Ulrich Krengel
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Editor information

Ulrich Krengel Karin Richter Volker Warstat

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© 1992 Springer-Verlag

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Hill, T.P., Krengel, U. (1992). On the construction of generalized measure preserving transformations with given marginals. In: Krengel, U., Richter, K., Warstat, V. (eds) Ergodic Theory and Related Topics III. Lecture Notes in Mathematics, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097531

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  • DOI: https://doi.org/10.1007/BFb0097531

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55444-8

  • Online ISBN: 978-3-540-47076-2

  • eBook Packages: Springer Book Archive

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