Sobolev regularity of occupation measures and paths, variability and compositions

We prove a result on the fractional Sobolev regularity of composition paths low with functions bounded variation. The relies notion variability, proposed by us in previous article [43]. Here we work under relaxed hypotheses, formulated terms norms, and can allow discontinuous paths, which is new. applies to typical realizations certain Gaussian or Lévy processes, use it show existence Stieltjes type integrals involving compositions.