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