Year: 2026
Type: article
Abstract: 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 (2014), 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 analogs of the Itô or Tanaka–Meyer formulas. Some of these formulas were already given by Bertoin and Yor (2014), but we also present some generalizations.
Source: Colloquium Mathematicum
Authors: Darlington Hove, Farai J. Mhlanga, Rafał M. Łochowski, Phumlani L. Zondi
Institutions: University of Limpopo, SGH Warsaw School of Economics
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4398795078