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Extension of stationary stochastic processes
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  • Published: March 1994

Extension of stationary stochastic processes

  • Barbara Kamm1 &
  • Andreas schief1 

Probability Theory and Related Fields volume 100, pages 77–84 (1994)Cite this article

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Summary

LetX be an arbitrary Hausdorff space, and consider a stationary stochastic process inX with time interval [0, 1], i.e. a tight probability onX [0, 1], equipped with the Borel σ-field of the product space. We prove the existence of a stationary extension of this process to ℝ +0 . Furthermore, we show that the extended process may be chosen to have continuous paths if the original process has this property. Under stronger topological assumptions, we derive the corresponding results whenX [0, 1] is equipped with the product of the Borel σ-fields.

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Authors and Affiliations

  1. Department of Mathematics, Ludwig-Maximilians-Universität, Theresienstrasse 39, D-80333, Munich, Germany

    Barbara Kamm & Andreas schief

Authors
  1. Barbara Kamm
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  2. Andreas schief
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Additional information

Corporate Research and Development, SIEMENS AG, D-81730 Munich, Germany

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Cite this article

Kamm, B., schief, A. Extension of stationary stochastic processes. Probab. Th. Rel. Fields 100, 77–84 (1994). https://doi.org/10.1007/BF01204954

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  • Received: 20 December 1993

  • Revised: 07 March 1994

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01204954

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Mathematics Subject Classification

  • 60G10
  • 28A35
  • 60B05
  • 28C15
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