Abstract
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 ℝ0+. 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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