2024/05/21 by Hove, Darlington, Mhlanga, Farai J., Łochowski, Rafał M. +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.13174
In this note, we define the numbers of level crossings by a càdlàg (RCLL) real function x: [0,+∞) → R and, in analogy to the work of Bertoin and Yor [BY14] we prove that for x with locally finite total variation these numbers are densities of relevant occupation measures associated with x. Next, depending on the regularity of x and f: R → R, we derive change of variable formulas, which may be seen as analogous of the Itô or Tanaka-Meyer formulas. Some of these formulas are present in [BY14] but we also present some generalizations.