Summary
We show that not all liftings are suitable tools for the regularization of stochastic processes. Under Continuum hypothesis, we construct a Glivenko-Cantelli class Z on [0, 1] and a lifting ρ ofL ∞ such that ρZ is not a Glivenko-Cantelli class. This strongly contrasts with the fact, shown earlier by the author, that some special liftings have exellent regularization properties.
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Talagrand, M. On liftings and the regularization of stochastic processes. Probab. Th. Rel. Fields 78, 127–134 (1988). https://doi.org/10.1007/BF00718040
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DOI: https://doi.org/10.1007/BF00718040
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Suitable Tool
- Regularization Property