Sobolev regularity of occupation measures and paths, variability and compositions

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Abstract

We prove a result on the fractional Sobolev regularity of composition of paths of low fractional Sobolev regularity with functions of bounded variation. The result relies on the notion of variability, proposed by us in the previous article [43]. Here we work under relaxed hypotheses, formulated in terms of Sobolev norms, and we can allow discontinuous paths, which is new. The result applies to typical realizations of certain Gaussian or Lévy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.
Original languageEnglish
Article number73
Pages (from-to)1–29
JournalElectronic Journal of Probability
Volume27
Issue number73
DOIs
Publication statusPublished - 15 Jun 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • 111 Mathematics

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