Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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On The Dichotomy of Stationary and Ergodic Probability Measures

  • Park, Jeong-Soo (Department of Statistics, Chonnam National University, 300 Yongbong-dong)
  • Published : 1993.12.01
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Abstract

The dichotomy of absolute continuity and singularity for a pair of stationary and ergodic measures (one of which need not be ergodic) is obtained using the ergodic decomposition theorem. The known fact that two different stationary and ergodic measures are mutually singular is obtained as a corollary of our result. An example of a pair of stationary-ergodic measures enjoying the dichotomy is presented.

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References

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