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- W4307533981 abstract "The paper deals with moduli of continuity for paths of random processes indexed by a general metric space $Theta$ with values in a general metric space $mathcal{X}$. Adapting the moment condition on the increments from the classical Kolmogorov-Chentsov theorem, the obtained result on the modulus of continuity allows for Holder-continuous modifications if the metric space $mathcal{X}$ is complete. This result is universal in the sense that its applicability depends only on the geometry of the space $Theta$. In particular, it is always applicable if $Theta$ is a bounded subset of a Euclidean space or a relatively compact subset of a connected Riemannian manifold. The derivation is based on refined chaining techniques developed by Talagrand. As a consequence of the main result a criterion is presented to guarantee uniform tightness of random processes with continuous paths.This is applied to find central limit theorems for Banach-valued random processes." @default.
- W4307533981 created "2022-11-03" @default.
- W4307533981 creator A5073241236 @default.
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- W4307533981 date "2021-07-29" @default.
- W4307533981 modified "2023-10-14" @default.
- W4307533981 title "A general Kolmogorov-Chentsov type theorem on general metric spaces with applications to limit theorems for Banach-valued processes" @default.
- W4307533981 doi "https://doi.org/10.48550/arxiv.2107.13837" @default.
- W4307533981 hasPublicationYear "2021" @default.
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