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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Corporate Research and Development, SIEMENS AG, D-81730 Munich, Germany
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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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DOI: https://doi.org/10.1007/BF01204954
Mathematics Subject Classification
- 60G10
- 28A35
- 60B05
- 28C15