3 papers
math.PR2025
The It{ô}-Föllmer formula -- nonstandard cases
W. M. Bednorz, R. M. Åochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the cà dlà g paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partit…
math.CA2025
Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)
Phumlani L. Zondi, Darlington Hove, RafaÅ M. Åochowski +1
We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}…
math.CA2024
Local times of deterministic paths with finite variation
Darlington Hove, Farai J. Mhlanga, RafaÅ M. Åochowski +1
In this note, we define the numbers of level crossings by a c{Ã }dl{Ã }g (RCLL) real function and, in analogy to the work of Bertoin and Yor [BY14] w…